Question

Show work/reason for answer if possible 5. Consider X~ Normal (7, 32) independent of Y~ Normal...

Show work/reason for answer if possible

5. Consider X~ Normal (7, 32) independent of Y~ Normal (5, 22). Which one of the following statements is not true?

A) E(X -Y) = 2

B) E(2X –Y+3) = 12

C) V(X +Y) = 32 +22

D) V(X -Y) = 32 +22

E) X+Y still a normal random variable

F) X -Y still a normal random variable

G) 3X is still a normal random variable

H) 3X+5 is still a normal random variable

I) P[X –Y-2 > 0] < 50%

J) P[X –Y-2 = 0] = 0.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Show work/reason for answer if possible Q4. An insurance company offers its policyholders a number of...
Show work/reason for answer if possible Q4. An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The CDF of X is given as follows: F[x]= 0      x<2 0,2    2<=x<4 0,4    4<=x<=6 1        x>=6 Also let Y = Min [2X+1, 6] Which one of the following is not true? Hint: Find the PMF of X first, then PMF of Y....
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5...
Given a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? A) V[Y] = 0.25. B) E[XY] = 0. C) E[X3] = 0. D) E[X+2] = 2. E) E[Y+2] = 2.5. F) E[W+2] = 4.5. G) V[X+2] = 0.5. H) V[W+2] = 0.25. I) P[W=1] = 0.5 J) X and W are not independent.
Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2, and E[X2]=E[Y2]=E[Z2]=5. Find cov(XY,XZ). (Enter a...
Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2, and E[X2]=E[Y2]=E[Z2]=5. Find cov(XY,XZ). (Enter a numerical answer.) cov(XY,XZ)= Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X. Is Y normal? Justify your answer. yes no not enough information to determine Compute Cov(X,Y). Cov(X,Y)= Are X and Y independent? yes no not...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent random variable following an identical distribution f(x):=e^(-x) if x>0, calculate the moment generating function of 2X+3Y b) If X follows a bernoulli(0.5), and Y follows a Binomial(3,0.5), and if X and Y are independent, calculate the probability P(X+Y=3) and P(X=0|X+Y=3)
X and Y are independent random variables. The mean and variance of X are 2 and...
X and Y are independent random variables. The mean and variance of X are 2 and 1 respectively. The mean and variance of Y are 3 and 2 respectively. Which of the statements below about the random variable X-Y is true? a. X-Y~Normal(-1,1) b. X-Y~Normal(1,3) c. X-Y has mean -1 and variance 3. d. X-Y has mean 5 and variance 3.
1.) Consider two independent discrete random variables X and Y with V(X)=2 and V(Y)=5. Find V(4X-8Y-9)....
1.) Consider two independent discrete random variables X and Y with V(X)=2 and V(Y)=5. Find V(4X-8Y-9). 2.) Consider two independent discrete random variables X and Y with SD(X)=16 and SD(Y)=9. Find SD(5X-2Y-13). (Round your answer to 1 place after the decimal point). 3.)Consider two discrete random variables X and Y with V(X)=81 and V(Y)=36 and correlation ρ=0.7. Find V(X-Y). (Round your answer to 1 digit after the decimal point).
Consider independent random variables X and Y , such that X has mean 2 and standard...
Consider independent random variables X and Y , such that X has mean 2 and standard deviation 4, and Y has mean 1 and standard deviation 9. Find the mean and standard deviation of the following random variables. a) 3X b) Y + 6 c) X + Y d) X − Y e) X1 + X2, where X1, X2 are independent copies of X.
(a) TRUE / FALSE If X is a random variable, then (E[X])^2 ≤ E[X^2]. (b) TRUE...
(a) TRUE / FALSE If X is a random variable, then (E[X])^2 ≤ E[X^2]. (b) TRUE / FALSE If Cov(X,Y) = 0, then X and Y are independent. (c) TRUE / FALSE If P(A) = 0.5 and P(B) = 0.5, then P(AB) = 0.25. (d) TRUE / FALSE There exist events A,B with P(A)not equal to 0 and P(B)not equal to 0 for which A and B are both independent and mutually exclusive. (e) TRUE / FALSE Var(X+Y) = Var(X)...
True or false? and explain please. (i) Let Z = 2X + 3. Then, Cov(Z,Y )...
True or false? and explain please. (i) Let Z = 2X + 3. Then, Cov(Z,Y ) = 2Cov(X,Y ). (j) If X,Y are uncorrelated, and Z = −5−Y + X , then V ar(Z) = V ar(X) + V ar(Y ). (k) Let X,Y be uncorrelated random variables (Cov(X,Y ) = 0) with variance 1 each. Let A = 3X + Y . Then, V ar(A) = 4. (l) If X and Y are uncorrelated (meaning that Cov[X,Y ] =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT