the joint density function of x and y is given by f(x y)=xe−x(y 1) x 0 y 0
Answers
The given joint density function of x and y is f(x,y) = xe-x(y+1), where x > 0, y > 0.
The marginal density function of X can be determined by integrating f(x,y) over all values of y as follows:f(x) = ∫₀^∞ f(x,y) dySo,f(x) = ∫₀^∞ xe-x(y+1) dy= xe-x ∫₀^∞ (y+1) e-xy dyLet u = xy + 1, dv = e-xy dyThen du/dy = x, v = -e-xyTherefore, using integration by parts formula,∫₀^∞ (y+1) e-xy dy = [(y+1)(-e-xy)]₀^∞ - ∫₀^∞ (-e-xy) dy= 0 + e-xy|₀^∞= 0 - e⁰= 1Hence, f(x) = xe-x ∫₀^∞ (y+1) e-xy dy= xe-x [1]= xe-x; x > 0Therefore, the marginal density function of X is given by f(x) = xe-x, where x > 0.The given joint density function of x and y is f(x,y) = xe-x(y+1), where x > 0, y > 0.
To find the marginal density function of X, we need to integrate the joint density function over all values of y as follows:f(x) = ∫₀^∞ f(x,y) dySo,f(x) = ∫₀^∞ xe-x(y+1) dy= xe-x ∫₀^∞ (y+1) e-xy dyTo evaluate the integral, we can use the integration by parts formula. Let u = xy + 1, dv = e-xy dy.Then, du/dy = x, and v = -e-xyApplying the integration by parts formula,∫₀^∞ (y+1) e-xy dy = [(y+1)(-e-xy)]₀^∞ - ∫₀^∞ (-e-xy) dy= 0 + e-xy|₀^∞= 0 - e⁰= 1Therefore, f(x) = xe-x ∫₀^∞ (y+1) e-xy dy= xe-x [1]= xe-x; x > 0Thus, the marginal density function of X is given by f(x) = xe-x, where x > 0.
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Related Questions
If a school district takes a random sample of 68 Math SAT scores and finds that the average is 500, and knowing that the population standard deviation of Math SAT scores is intended to be 100. Find a 99% confidence interval for the mean math SAT score for this district
Answers
The 99% confidence interval for the mean math SAT score for this district is [468.80, 531.20]. We can be 99% confident that the true mean math SAT score for the district is within this interval.
To calculate the confidence interval, we will use the formula:
CI =\(\bar x\) ± zα/2 × (σ/√n)
where:
\(\bar x\) is the sample mean (500)
zα/2 is the z-score for the desired confidence level (99%, which corresponds to a z-score of 2.576 for a two-tailed test)
σ is the population standard deviation (100)
n is the sample size (68)
Plugging in the values, we get:
CI = 500 ± 2.576 × (100/√68)
CI = 500 ± 2.576 × 12.11
CI = 500 ± 31.20
Therefore, the 99% confidence interval for the mean math SAT score for this district is [468.80, 531.20]. We can be 99% confident that the true mean math SAT score for the district is within this interval.
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Which of these statements best describes a biased sample?
A. The sample is small
B. The sample has results that are incorrect predictions
C. The sample does not accurately represent the population
D. The sample was chosen randomly
Answers
A biased sample is best described by:
C. The sample does not accurately represent the population.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample, which is a group of members of this population. The sample has to be representative of the population, that is, it has to involve all of it's groups. If it does not involve all the groups, it is not an accurate representation of the population, and is called biased, hence option C is correct.
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The slope is -1 and the y-intercept is -5. Write a linear equation in slope-intercept form.
Someone pls help me!
Answers
\(y = mx + b\)
where m = slope and b = y-intercept.
We have both given slope and y-intercept. We can simply substitute the given slope and y-intercept in slope-intercept form.
SubstitutionSubstitute m = -1 and b = - 5 in the equation.
\(y = - 1x - 5 \\ y = - x - 5\)
We don't usually write 1x or -1x instead we write -x or x.
Answer\(y = - x - 5\)
Graph the function f(x)=3/2x-4. Use the line tool and select two points to graph.
Answers
Answer:
Slope = 3/2
y-intercept = -4
x | y
0 -4
2 -1
Step-by-step explanation:
Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
Answers
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:
tan θ = -5/12
θ = 180 -tan⁻¹-(5/12)
θ = 157.38
sin θ/2 = sin 157.38/2
sin θ/2 = 0.9806
tan θ/2 = tan 157.38/2
tan θ/2 = 4.99
In conclusion, the values of the sine and tangent are found from the given values.
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help me please click image to see problem
Answers
Answer:
option 1...............
When President Dwight Eisenhower ordered the Arkansas National Guard into service to enforce court orders to desegregate schools, it was an example of a. executive orders. b. political mandate. c. gerrymandering. d. cloture. e. filibustering.
Answers
When President Dwight Eisenhower ordered the Arkansas National Guard into service to enforce court orders to desegregate schools, it was an example of a) executive orders.
Executive orders are directives issued by the President of the United States that have the force of law. They are used to manage and govern the operations of the federal government. In this case, President Eisenhower used his executive authority to deploy the Arkansas National Guard to enforce the desegregation of schools as mandated by the courts.
The Supreme Court's landmark decision in Brown v. Board of Education in 1954 declared that segregation in public schools was unconstitutional. However, resistance to desegregation persisted in some areas of the country, including Arkansas. To ensure compliance with the court's ruling, President Eisenhower exercised his executive power and deployed the National Guard to Little Rock, Arkansas, to protect and enforce the rights of African American students seeking to attend previously all-white schools.
Therefore, President Eisenhower's action of ordering the Arkansas National Guard to enforce court orders to desegregate schools falls under the category of a) executive orders, as he used his executive authority to implement a policy decision.
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6(x+4)+3(x−2)
Show your work.plzzzz hurryyyy!!!!
Answers
Answer: 9x +18
Step-by-step explanation: It simplifies to 6x + 24 +3x -6, which then simplifies to 9x +18.
Step by Step:
Rewrite :6(x+4)+3(x-2)
Distribute each side: 6x+24 + 3x-6
Do like terms: 6x+3x= 9x 24-6=18
Final Answer: 9x+ 18
PLEASE HELP
Is this graph proportional or non
Group of answer choices
Proportional
non-proportional
Answers
Answer:
I dont see a picture-
Step-by-step explanation:
6) Write a function that can be used to represent
the total cost of apples purchased if one pound
Answers
Answer:453.59237
Step-by-step explanation: we know that each apple weighs 120 grams so we can add them up to get 453.59237 it would take about 3 apples to get 453.59237 so 453.59237 is our awnser
For the expression 2-2a to have a negative value, what must be true about the value of a?
Answers
What must be true about the value of a is that is must be greater than 1
How to determine the expressionIt is important to note that algebraic expressions are those expressions that are consisting of terms, coefficients, factors, constants and variables.
They are identified with arithmetic operations like;
AdditionBracketParenthesesDivisionMultiplicationSubtractionFrom the information given, we have the expression;
2-2a
To get a negative value, a = 2
2 - 2(2)
2 - 4
subtract the values
-2
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Carlos has 38 apples. He puts 8 apples into each bag if he fills as many bags as possible, how many apples are left
Answers
Answer:
6
Step-by-step explanation:
What you need to do is 38 ÷ 8. The answer would be 4 with a remainder of 6, so there are six apples left
picture above
give the right answer and i’ll literally give 75 extra points and brainliest x2 , please help i can’t fail
Answers
Answer:
False :)
Step-by-step explanation:
Answer:
Not a function, therefore false.
Step-by-step explanation:
Maybe this attachment can help.
Look at the triangles. What information is needed to prove that △ABC∼△DEF?
Options are listed at the bottom
Answers
Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
AB and DE, BC and FE, then AC and DF
The solution is worked out using sides BC and FE, then AC and DF
BC / AC = FE / DF
8 / AC = 16 / 20
reducing the fraction 16/20 gives
8 / AC = 8 / 10
hence AC = 10
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At age 45 when the deferred payments from his current contract ends, all-star shortstop Alex Rodriguez plans to have $230 million in savings from his baseball playing days. He wants two things from his savings: a 40-year ordinary annuity and $500 million at age 60 in order to purchase majority ownership in his native Miami's Florida Marlins. How large can his annual annuity payment be based on this information and assuming his savings can earn 8% annually after age 45 ? $6,069,727 $5,620,118 $6,906,832 $6,395,215
Answers
Therefore, the annual annuity payment can be approximately $6,069,727.
To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:
PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]
Where:
PMT = Annual annuity payment
PV = Present value of the annuity
r = Annual interest rate
n = Number of periods
Given:
PV = $230 million
r = 8% = 0.08
n = 40 years
Using the formula, we can calculate the annual annuity payment:
PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]
PMT ≈ $6,069,727
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Use the divergence theorem to calculate the flux of the vector field F⃗ (x,y,z)=x3i⃗ +y3j⃗ +z3k⃗ out of the closed, outward-oriented surface S bounding the solid x2+y2≤25, 0≤z≤4
Answers
The flux of the vector field F⃗ (x,y,z)=x3i⃗ +y3j⃗ +z3k⃗ out of the closed, outward-oriented surface S bounding the solid x2+y2≤25, 0≤z≤4 is 0.Therefore, the flux of F⃗ out of the surface S is 7500π.
To use the divergence theorem to calculate the flux, we first need to find the divergence of the vector field F. We have div(F) = 3x2 + 3y2 + 3z2. By the divergence theorem, the flux of F out of the closed surface S is equal to the triple integral of the divergence of F over the volume enclosed by S. In this case, the volume enclosed by S is the solid x2+y2≤25, 0≤z≤4. Using cylindrical coordinates, we can write the triple integral as ∫∫∫ 3r^2 dz dr dθ, where r goes from 0 to 5 and θ goes from 0 to 2π. Evaluating this integral gives us 0, which means that the flux of F out of S is 0. Therefore, the vector field F is neither flowing into nor flowing out of the surface S.
Now we can apply the divergence theorem:
∬S F⃗ · n⃗ dS = ∭V (div F⃗) dV
where V is the solid bounded by the surface S. Since the solid is described in cylindrical coordinates, we can write the triple integral as:
∫0^4 ∫0^2π ∫0^5 (3ρ2 cos2θ + 3ρ2 sin2θ + 3z2) ρ dρ dθ dz
Evaluating this integral gives:
∫0^4 ∫0^2π ∫0^5 (3ρ3 + 3z2) dρ dθ dz
= ∫0^4 ∫0^2π [3/4 ρ4 + 3z2 ρ]0^5 dθ dz
= ∫0^4 ∫0^2π 1875 dz dθ
= 7500π
Therefore, the flux of F⃗ out of the surface S is 7500π.
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h(j + i) - k5 + h
when h = 3, i = 4, j = 2, and k = 1
pls put how you did it
Answers
Answer:
16
Step-by-step explanation:
First you want to plug in all the numbers where the letters are
h ( j + i )- k(5) + h
3 ( 2 + 4 )- 1(5) + 3
After this step you will have to distribute the 3 outside the parenthesis. Which you do by multiplying everything in side the parenthesis by the outside number which is three.
6 + 12 - 1(5) + 3
Then you just follow PEMDAS to solve for the rest
6 + 12 - 5 + 3
18 - 5 + 3
13 + 3
16
Luna mixescup of orange juice with cup of cranberry juice. She gives
cup of the juice to Mags. How much is left in Luna's glass?
Answers
the amount of juice left in Luna's glass is 1/2.
We have been given that Luna mixes 3/4 cup of orange juice with 3/8 cup of cranberry juice.
First of all, let us find the total amount of juice Luna had by adding the amount of orange juice to amount of cranberry juice.
Total amount of juice Luna had = 3/4 + 3/8
= 9/8
Since Luna gave 5/8 cup of juice to Mags, so let us subtract amount of juice given to Mags from the total amount of juice to find the amount of juice left in Luna's glass.
Hence, Amount of juice left in Luma glass is,
= 9/8 - 5/8
= 4/8
= 1/2
Therefore, the amount of juice left in Luna's glass is 1/2.
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17. priti wants to wish her 5 subject teachers by giving them a self-made greeting card on teacher's day. she has chosen a green colored square sheet of paper.a side of that paper measures 20.5 cm. what is the area of each card? ii) find the edge of each card correct to two decimal places
Answers
The area of each card is 80.05cm^2, and the edge of each card is 8.95cm.
Priti chose a green coloured square paper of 20.5cm, since its a square the length and breadth of the card are equal
l = b
Recall the area of a square is
A = l^2
A = (20.5)^2
A= 20.5 × 20.5
A= 400.25cm^2
Since the paper is to be used for 5 cards, therefore the is divided in 5 equal cards. The are area of each card will be
A = A/5
A = 400.25/5
A = 80.05cm^2
The edge of each card is the side of the each card which can either be the length or the breadth since all the sides are equal for a square.
Recall that
A = l^2
Since the Area of each card is 80.05cm^2. Therefore,
80.05 = l^2
Finding the square root of both sides
(80.05)^1/2 = (l^2)^1/2
l = 8.947cm
Approximate l to 2 decimal place
l = 8.95cm
Therefore, the edge of each card is 8.95cm
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7x-3 = 5x+ 15
I have to write an explanation for this problem using the words variable term and constant term... can someone help me?
Answers
Answer:
7x-3 = 5x+ 15
2x-3 = 15 (you will need to subtract the variables to get 2x)
2x = 18 (next, add the constants to result up to 18)
x = 9 (lastly, divide the constant 18 with the coefficient 2 to get 9)
A circle has centre (-3,-4) and a point P(5,2) on its circumference. Determine the equation of the circle expressed in the form x²+y²+ax+by+c=0
Answers
The equation of the circle expressed in the form x²+y²+ax+by+c=0 is (x+3)² + (y+4)² - 100 = 0.
Center of the circle = (-3,-4)Point on the circumference of the circle = P(5,2) We know that the equation of the circle is given by: (x−a)²+(y−b)²=r² where the center of the circle is (a, b) and the radius is r.
Step 1: Find the radius of the circle using the distance formula Distance between the center of the circle and point
P = radius of the circle.
We get
r = √((-3-5)² + (-4-2)²)r = √64+36r = √100 = 10
Step 2:Find the equation of the circle substituting the center and the radius into the equation of the circle
(x−a)²+(y−b)²=r²(x-(-3))² + (y-(-4))² = 10²(x+3)² + (y+4)² = 100(x+3)² + (y+4)² - 100 = 0
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Please help 25 points
Answers
You must decide whether to buy new machinery to produce product X or to modify existing machinery. You believe the probability of a prosperous economy next year is 0.7. Prepare a decision tree and use it to calculate the expected value of the buy new option. The payoff table is provided below (+ for profits and - for losses).
When entering the answer, do not use the $ symbol. Do not enter the thousand separator. Enter up to 2 decimal places after the decimal point. For example, $6,525.35 must be entered as 6525.35
N1: Prosperity ($) N2: Recession ($)
A1 (Buy New) $1,035,332 $-150,000
A2(Modify) $823,625 $293,648
Answers
The expected value of the "Buy New" option is 724732.60.
Decision Tree:
To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:
Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:
Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)
Substituting the given values in the above formula, we get:
Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60
Therefore, the expected value of the "Buy New" option is 724,732.60.
Conclusion:
To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.
The expected value of the "Buy New" option is 724,732.60.
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The graph of a quadratic function having the form f(x) = ax? + bx + c passes
through the points (0, -8), (3, 10), and (6,34). What is the value of the function
when x = -3?
Answers
Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
_____
The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
PLEASE HELP DUE TODAY HELP ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
it's the first one
Step-by-step explanation:
you'd get each output (y) when you subtract 4 from whatever x is
Joel made a scale drawing of a boarding school. A building at the school is 16 millimeters wide in the drawing. The actual building is 20 meters wide. What is the scale of the drawing?
Answers
Answer:
Step-by-step explanation:
.8 millimeters :1 meters
Answer: 5 METERS ACCORDING TO IXL
Step-by-step explanation:
3
—
4 divided by
9
—
10
Answers
Answer:
\(\displaystyle \frac{\frac{3}{4}}{\frac{9}{10}}=\frac{5}{6}\)
Step-by-step explanation:
Fraction Division
The division of two fractions a/b and c/d is usually done by multiplying the first fraction by the reciprocal of the second fraction:
\(\displaystyle \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\cdot\frac{d}{c}\)
We are required to divide:
\(\displaystyle \frac{\frac{3}{4}}{\frac{9}{10}}\)
Applying the above rule:
\(\displaystyle \frac{\frac{3}{4}}{\frac{9}{10}}=\frac{3}{4}\cdot\frac{10}{9}=\frac{30}{36}\)
Simplifing by 6:
\(\boxed{\displaystyle \frac{\frac{3}{4}}{\frac{9}{10}}=\frac{5}{6}}\)
this is for the brainlist winner
Answers
Does this shape have rotational, reflection, both or none
Answers
A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine.
Answers
Using the properties of mean and standard deviation, the mean of the total volume of the beverage in the case is 480.24 ounce and the standard deviation of the total volume of the beverage in the case is 0.48 ounce.
Mean is the average of all numbers given. Whereas, standard deviation is the measure of spread of the numbers.
The properties of mean and standard deviation used :
\(\mu_{aX+b} = a\mu+b\\\\\sigma_{aX+b} = a\sigma+b\\\)
Given,
mean of fill volume of bottles = 20.01 ounce
standard deviation of fill volume of bottles = 0.02 ounce
number of bottles in case = 24
Using the properties above:
mean of case = number of bottles in case * mean of fill volume of bottles = 24 * 20.01 = 480.24 ounce
standard deviation of case = number of bottles in case * standard deviation of fill volume of bottles = 0.02 * 24 = 0.48 ounce
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complete question is given below:
A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine. a. Find the mean of the total volume of the beverage in the case. b. Find the standard deviation of the total volume of the beverage in the case.