Two ballpoint pens were randomly selected from a box containing 3 green ballpoint pens, 2 red ballpoint pens and 3 blue ballpoint pens. If the number of blue ballpoint pens selected is stated by X and Y
a. Specify the expected value of g(X,Y)=XY
b. Specify the covariance of X and Y
Answers
If the number of blue ballpoint pens selected is stated by X and Y, then:
a. Expected value of g(X,Y) = E(g(X,Y)) = 3/4
b. Covariance of X and Y = Cov(X,Y) = 3/16.
The given box contains 3 green ballpoint pens, 2 red ballpoint pens and 3 blue ballpoint pens. If the number of blue ballpoint pens selected is stated by X and Y, then:
a) The expected value of g(X,Y)=XY is as follows:
There are 8 ballpoint pens in the box and two are randomly selected.
There can be three possible cases here:
2 blue pens1 blue and 1 non-blue pen2 non-blue pensThe probability of getting 2 blue pens is given by:
P(X=2,Y=2) = (3/8) (2/7) = 6/56 = 3/28
The probability of getting 1 blue and 1 non-blue pen is given by:
P(X=1,Y=1) = (3/8) (5/7) + (5/8) (3/7) = 15/56 + 15/56 = 15/28
The probability of getting 2 non-blue pens is given by:
P(X=0,Y=0) = (5/8) (4/7) = 20/56 = 5/14
Expected value of g(X,Y)=XY is:E(g(X,Y)) = ΣxyP(X=x,Y=y) = 2(3/28) + 1(15/28) + 0(5/14) = 3/4
b) The covariance of X and Y is:
Cov(X,Y) = E(XY) - E(X)E(Y)E(X) is given by:
E(X) = ΣxP(X=x) = 0(5/14) + 1(15/28) + 2(3/28) = 3/4
E(Y) is given by: E(Y) = ΣyP(Y=y) = 0(5/14) + 1(15/28) + 2(3/28) = 3/4
E(XY) is given by: E(XY) = ΣxyP(X=x,Y=y) = 2(3/28) + 1(15/28) + 0(5/14) = 3/4
Now, Cov(X,Y) = E(XY) - E(X)E(Y) = (3/4) - (3/4)(3/4) = 3/16
Hence, the required values are: E(g(X,Y)) = 3/4, Cov(X,Y) = 3/16.
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Related Questions
Express 16 as a product of its prime factors.
Answers
Answer:
16 = 1 x 16, 2 x 8, or 4 x 4. Factors of 16: 1, 2, 4, 8, 16. Prime factorization: 16 = 2 x 2 x 2 x 2,
Step-by-step explanation:
which can also be written 16 = 2⁴. Since √16 = 4, a whole number, 16 is a perfect square
if this helped please give me brainliest
Answer:
It will be:
Step-by-step explanation:
16=:
a) 1 x 16
b) 2 x 8
c) 4 x 4
All these are the product of 16 prime factors.
Prime factors are any of the number that can be multiplied to give the original number.
Hope they help.
First correct answer will get brainliest!!!!!!
Lakesha has $63 to spend at a supermarket. She spends 1/3 of her money buying vegetables. How much money does she spend on vegetables?
incorrect answers, etc will be deleted and reported.
Answers
Answer:
$21
Step-by-step explanation:
We need to find out 1/3 of 63.
63*1/3=21
So 63-21=$42
Lakesha spent $21 on vegtables (and has $42 left.)
If any pair of three lines are parallel, then are all three lines are coplanar?
Parallel Lines - Lines that never intersect
Coplanar - Points that lie in a plane
Answers
Answer: False
Step-by-step explanation:
you can have 3 lines that are parallel and them not be coplanar
Number One in the photo provided
Answers
a. np = 8.91 and nq = 18.09 where n = 27 and p = 0.33
b. np = 3.75 and nq = 21.25 where n = 25 and p = 0.15
c. np = 9.68 and nq = 34.32 where n = 44 and p = .22
Solution:a. Given n = 27
p = 0.33
np = 27 x 0.33
= 8.91
nq = 27 x (1 - 0.33)
= 18.09
For the approximation of binomial distribution, the sample size must be greater than 10 for both the products np and n(1-p) to approximate the binomial distribution by a normal distribution.
Since here np < 10 approximation is not applicable.
μp = np = 27 x 0.33
= 8.91
σp = √npq = √(27)x (.33) x (1 - 0.33)
= 2.443
b. n = 25 and p = 0.15
np = 25 x 0.15
= 3.75
nq = 25 x (1 - 0.15)
= 21.25
Approximation is not possible because np < 10.
c. n = 44 and p = .22
np = 44 x 0.22
= 9.68
nq = 44 x (1 - 0.22)
= 34.32
Since here np< 10 approximation is not possible.
μp = np = 44 x 0.22
= 9.68
σp =√npq = √(44)x (.22) x (1 - 0.22)
= 2.747
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the sum of two number 12 when three times the first number is added to 5 times the second number the results is 44
Answers
Answer:
one number is 8 and other is 4
Step-by-step explanation:
So we can say x+y=12.
And 3x+5y=44
For x+y=12, we can subtract x to get: y=12-x
Plug that in to get 3x+5(12-x)=44
3x+60-5x=44
Subtract 44: -2x+16=0
2x=16
x=8
12-8=4.
Gavin and Ethan are training for a race. Last week, Gavin ran 7 kilometers, and Ethan ran twice as far as Gavin. What is the total distance that Gavin and Ethan ran last week? Express your answer in meters.
Answers
If Ethan ran twice as far as Gavin then he ran 14 kilometers. 7*2=14. And then you add 7 to 14 which gives you 21. so they ran a total of 21 kilometers
The total distance that Gavin and Ethan ran last week is 21000 meters.
Given that, Gavin and Ethan are training for a race.
What is total?A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.
Last week, Gavin ran 7 kilometers, and Ethan ran twice as far as Gavin.
Number of kilometers Ethan ran =2×7
= 14 kilometers
= 14×1000
= 14,000 meters
Now, 7 kilometers = 7000 meters
Total =14000+7000
= 21000 meters
Therefore, the total distance that Gavin and Ethan ran last week is 21000 meters.
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lilian's favorite magazine published 505050 issues last year, and each issue contained approximately 250250250 pages. she wants to take a cluster random sample of about 1{,}0001,0001, comma, 000 total pages to estimate what proportion of all pages contained an advertisement. which of these strategies will accomplish her intended design?
Answers
Lilian will be able to obtain a representative sample of about 1,000 pages, which she can then use to estimate the proportion of all pages that contain an advertisement.
To accomplish Lilian's intended design of estimating the proportion of pages containing an advertisement, she can use the following strategy:
Cluster Sampling:
In cluster sampling, the population is divided into clusters, and a random selection of clusters is made. In this case, the clusters would be the individual issues of the magazine. Lilian can randomly select a subset of issues as clusters for her sample.
1. Divide the total number of pages in all issues (505050 x 250250250) to get the total number of pages.
2. Randomly select 1,000 pages from the total number of pages obtained in step 1 using a cluster random sampling method.
3. Determine the number of pages in each selected issue. Multiply this number by the total number of selected issues to obtain the total number of pages in the sample.
4. Estimate the proportion of all pages containing an advertisement by counting the number of pages with advertisements in the selected sample and dividing it by the total number of pages in the sample.
By following this strategy, Lilian will be able to obtain a representative sample of about 1,000 pages, which she can then use to estimate the proportion of all pages that contain an advertisement.
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Find the percent of increase from 40 gallons to 89 gallons. Round to the nearest tenth of a percent if necessary.
percent of increase?
Answers
Answer:
50
Step-by-step explanation:
because 89-49=49 49 rouded to the nearest ten is 50
Select all of the equations below that are equivalent to:
16 + m = 8
Use properties of equality.
Answers
Answer:
All of them
Step-by-step explanation:
We can start from the top left.
To get from 16 + m to 16 + m - 2 on the left side of the equation, we can subtract 2 from 16 + m. Using the subtraction property of equality, we then must also subtract 2 from the right side. Doing this, we get
16 + m - 2 = 8 - 2
16 + m - 2 = 6
This matches up with the equation given
Next, for the top right equation, we can see that to get from 16 + m to 16 + m - 3, we must subtract 3. We can do this to both sides to get
16 + m - 3 = 8 - 3 = 5
This matches up with the equation
For the bottom left equation, we can subtract 5 from both sides to get
16 + m - 5 = 8 - 5 = 3
This matches up
For the bottom right equation, we can subtract 6 from both sides to et
16 + m - 6 = 8 - 6 = 2
This also matches up
f a graph had 16 vertices of odd valence, what is the absolute MINIMUM number of edges that would need to be added (duplicated) to eulerize the graph? 10 9. If a graph had 16 vertices of odd valence, what is the absolute MINIF 2 8 06 4 9. If a graph had 16 vertices of odd 2 8 06 4
Answers
The smallest number of edges that would need be duplicated to eulerize the graph is 8.
Here, we have,
Given that
a graph has 16 vertices.
now, we have to get the graph to be eulerized, it has to added an edge to each vertex having odd valence.
Here total number of vertices = 16
So, the smallest number which is of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.
Number of edges = 16/2 = 8
Hence it is needed 8 edges to eulerize the graph.
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write the precent of thse fractions and decimals ( write full ans )
Answers
Answer:
Step-by-step explanation:
dava kaAjbhm
SOMEONE HELP ASAP. THIS IS DUE IN A FEW HOURS AND THE LAST QUESTION I NEED.
It will be much appreciated, and I will add rewards
Ignore the 18/15=1.2, I am in a rush
Answers
Assumption 1: \(\triangle ABE \sim \triangle ACD/tex]
\(\frac{x}{10}=\frac{3}{15} \implies x=2\)
Assumption 2: \(\triangle ABE \sim \triangle ADC\)
\(\frac{x}{15}=\frac{3}{10} \implies x=4.5\)
student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
Answers
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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mrs jones surverys her class about their siblings. 75% have a brother, 82% have a brother, and 65% have a brother and a sister. what is the probability that a student has a brother or a sister
Answers
The probability that a student has a brother or a sister is: 92%
How to solve conditional probability?Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.
We are given the parameters as:
Percentage that have a brother = 75%
Percentage that have a sister = 82%
Percentage that have a brother and a sister = 65%
Thus:
P(Brother or Sister) = 0.75 + 0.82 - 0.65
P(Brother or Sister) = 0.92 = 92%
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It is known that X has a uniform distribution with μ=0.5 minutes and σ=0.29 minutes. Suppose a random sample of 64 people is selected. The shape of the sampling distribution of X
ˉ is: Uniform Approximately Normal Normal not enough information to determine
Answers
In this scenario, the shape of the sampling distribution of X-bar is approximately normal.
The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.
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Orthogonally diagonalize the matrix below by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D.(Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.)
Answers
To orthogonally diagonalize the matrix A, we will follow these steps:
1. Find the eigenvalues of matrix A.
2. Find the eigenvectors corresponding to each eigenvalue.
3. Normalize the eigenvectors to form an orthogonal basis.
4. Construct the orthogonal matrix Q and the diagonal matrix D.
To orthogonally diagonalize the matrix A, we need to find the eigenvalues and eigenvectors of A.
A = [[3, -1], [-1, 3]]
The characteristic polynomial of A is:
det(A - λI) = det([[3-λ, -1], [-1, 3-λ]]) = (3-λ)² - 1 = λ² - 6λ + 8 = (λ-2)(λ-4)
So the eigenvalues are λ₁ = 2 and λ₂ = 4.
To find the eigenvectors, we need to solve the system of equations:
(A - λ₁I)x = 0 and (A - λ₂I)x = 0
For λ₁ = 2, we have:
(A - 2I)x = [[1, -1], [-1, 1]]x = 0
This system has two linearly independent solutions:
v₁ = [1, 1] and v₂ = [-1, 1]
For λ₂ = 4, we have:
(A - 4I)x = [[-1, -1], [-1, -1]]x = 0
This system has one linearly independent solution:
v₃ = [1, -1]
To orthogonalize the eigenvectors, we need to normalize them and put them as columns of an orthogonal matrix Q.
Q = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]
The diagonal matrix D has the eigenvalues on the diagonal:
D = [[2, 0], [0, 4]]
Finally, we can check that QTAQ = D:
QTAQ = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]T[[3, -1], [-1, 3]][[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]] = [[2, 0, 0], [0, 4, 0], [0, 0, 4]] = D
Therefore, matrix A is orthogonally diagonalized by Q and D.
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Comeplete the equivalent equation of -7x-60=x(2)+10x
Answers
Answer:
\(3 \frac{3}{ 19} \)
WILL MARK BRAINLIEST IF CORRECT
Answers
Answer:
it is actually 70
Step-by-step explanation:
Answer:
72
Step-by-step explanation:
x + ( x + 2 ) + ( x + 4 ) = 210
3x + 6 = 210
3x = 204
x = 68
Remember that x is the smallest, so we have to add 4 to 68 to get the largest of the 3 consecutive even integers: 68 + 4 = 72.
3. Order each set of integers from least to greatest
a. 65, 61, 59, 45,2
b. 32, 78, 48, 33, 11
c. 99,86,5,63, 31,9
d. 79, 91, 32, 27, 20
Answers
B. 11,32,33,48,78
C. 5,9,31,63,86,99
D. 20,27,32,79,91
Mark as brainliest plz:)
B= 11, 32, 33, 48, 78
C= 5, 9, 31, 63, 86, 99
D= 20, 27, 32, 79, 91
Integers is just another name for numbers. :-)
The temperature one cold morning is -5 °C. By noon, the temperature had increased by 3 degrees and at 4 PM the temperature was zero. The increase from noon to 4 PM was
Answers
Answer:
2°C
Step-by-step explanation:
Morning
-5°C
Noon (+3)
-2°C
4pm (+?)
0°C
Equation I used:
(-5) + (3) + x = 0
I'm assuming you're being taught how to work with negative intervals in algebra? Don't worry, that's why you're practising with temperature. Instead of asking online, try using the progress your teacher taught you. If you have notes, look back at them. Practise makes perfect :)
I will give brainliest to one of the correct answers.
Marti rolls two dice. What is the probability that the sum of the dice is 7, given that the first die is showing a 2?
Please only answer if you know.
Answers
Answer:
1/6
Step-by-step explanation:
Since the first dice is already two the second one has to be 5, and there are 6 sides on a dice and one side that is 5, the probability is
1/6
a penny, nickel, and dime are all flipped once. what is the probability that at least one coin comes up heads?
Answers
Answer: 25% chance
Step-by-step explanation: the chance is 25 % because theirs 3 coins each equaling 25 So, all 3 added will equal 75 % and then, if the 1 coin landed on heads while the other 2 coins lands on heads that would minus 25% and 50% and get 25%.
hopefully u consider me as a giga chad :)
i need this quick!!
What are the constants in the equation 3x+2=9
a - 3
b - x
c - 2 and 9, constants have a fixed value
d - none of the above
Answers
Answer:
Option C i.e. 2 and 9, constants have a fixed value is a correct option.
Step-by-step explanation:
In algebra, a constant is basically a fixed value.
Sometimes, a constant is a number for a letter such as a, b, or c for a fixed number.
For example: in ''2x+7=3'', 7 and 3 are constants.
Please note that the number with variable x in the term is a coefficient.In our case:
Given the equation
\(3x+2=9\)
Therefore, 2 and 9 are constants, having a fixed value.
Thus, option C i.e. 2 and 9, constants have a fixed value is a correct option.
A car drives at 90km/h for 2 hours 20 mins. How far does the car drive?
Answers
Answer:
210 km
Step-by-step explanation:
anahqjakqkqkqkqk
Which temperature is greater, -20F or -60F
Answers
Answer:
-20
Step-by-step explanation:
Answer:
It's -20F :)
Step-by-step explanation:
hsbshehehebvdhshhakakkanabsbxh
true/false: a base class cannot contain a pointer to one of its derived classes.
Answers
The statement a base class cannot contain a pointer to one of its derived classes is false because a base class can indeed contain a pointer to one of its derived classes.
In object-oriented programming, a base class can have a pointer to one of its derived classes. This is known as upcasting or polymorphism. Upcasting allows for the flexibility of treating derived class objects as instances of the base class.
By using pointers, a base class can refer to derived class objects and access their member functions and variables. This enables the base class to work with different derived classes without needing to know their specific types.
Pointers to derived classes can be stored in base class member variables or passed as function parameters. This allows for dynamic binding and the ability to invoke overridden functions based on the actual derived class type at runtime.
This concept is fundamental to achieving polymorphism and code reusability in object-oriented programming languages like C++ and Java. It facilitates the implementation of inheritance hierarchies and the ability to work with objects of different derived classes through a common base class interface.
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Julie has four times as many pairs of shoes as her brother. Together they have 15 pairs of shoes. How many pairs of shoes do they each have?
Answers
Answer:
60 pairs of shoes
Step-by-step explanation:
To find the answer, multiply 4x15. The words four times as many mean to do the operation of multiplication. 4x15= 60 So finally, each have 60 pairs of shoes.
i hope this helped:)
Answer:
7.5
Step-by-step:
Julie: ?
Her brother: ?
Total number: 15
So: 15 divided to julie and her brother-
There for 15 divide by 2 is 7.5
7.5+7.5=15
if RS=2x+6 ST=x+4 and RT=40 find RS
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
\(undefined\)14a + 2 =
Please help
Answers
Answer: ( 2 x 7 ) a + 2
Step-by-step explanation:
write the equation of a line that passes through the point (4,-1/4) and has a slope of 0
Answers
Answer:
y = -1/4
Step-by-step explanation:
If the slope is o, that means that it is a horizontal line. The line passes though the point (4, -1/4) The horizontal line will have y as -1/4, no matter what x is.
Answer:
\(\sf y =\dfrac{-1}{4}\)
Step-by-step explanation:
Equation of the line with slope 0 is y = c.
where c is the y-co-ordinate.
The line with slope 0 is a horizontal line that is parallel to x-axis.
\(\sf y =\dfrac{-1}{4}\)