Question

In: Statistics and Probability

Let X and Y be two discrete random variables with a common mgf of e^(4t). After...

Let X and Y be two discrete random variables with a common mgf of e^(4t). After some analysis you conclude, X = 4 and Y = 6. Is this a valid claim? Why or why not?

Expert Solution

Let X and Y be two discrete random variables with a common mgf of . After some analysis we conclude, X = 4 and Y = 6.

=> Our claim is invalid.

Explanation:-

[ Formula for mgf:-

For a discrete random variable M, mgf of M is given by,

]

Now if X = 4, then mgf of 4 is given by,

and given that X = 4 has mgf .

So, by the question we get,

.................(1)

Now if X = 6, then mgf of 6 is given by,

and given that X = 6 has mgf .

So, by the question we get,

..................(2)

Now since, so the values of these two cannot be equal. i.e equation (1) and equation (2) can not satisfied simultaneously.

Answer:- This proof that our claim is invalid.

orchestra answered 2 years ago

Let X and Y be two discrete random variables with a common mgf of e^(4t). After...

Let X and Y be two discrete random variables with a common mgf of e^(4t). After some analysis you conclude, X = 4 and Y = 6. Is this a valid claim? Why or why not?

Let X and Y be jointly normal random variables with parameters E(X) = E(Y ) =...

Let X and Y be jointly normal random variables with parameters E(X) = E(Y ) = 0, Var(X) = Var(Y ) = 1, and Cor(X, Y ) = ρ. For some nonnegative constants a ≥ 0 and b ≥ 0 with a2 + b2 > 0 define W1 = aX + bY and W2 = bX + aY . (a)Show that Cor(W1, W2) ≥ ρ (b)Assume that ρ = 0.1. Are W1 and W2 independent or not? Why? (c)Assume now...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X)...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X) = var(Y) = 10. A new random variable is defined as: W = X+2Y+2. a. Find E[W] and var[W] if X and Y are independent. b. Find E[W] and var[W] if E[XY] = 20. c. If we find that E[XY] = E[X]E[Y], what do we know about the relationship between the random variables X and Y?

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y , taking values in {0, 1, 2, 3} each (for a total of 16 possible points). Their joint probability mass function is given by fXY (x, y) = c · x+1 y+1 . Answer the following questions. (a) What is c? (b) What is the probability that X = Y ? (c) Derive the marginal probability mass functions for both X and Y . (d)...

Let X and Y be two discrete random variables whose joint probability distribution function is given...

Let X and Y be two discrete random variables whose joint probability distribution function is given by f(x, y) = 1 12 x 2 + y for x = −1, 1 and y = 0, 1, 2 a) Find cov(X, Y ). b) Determine whether X and Y are independent or not. (Justify your answer.

Let X and Y be independent discrete random variables with the following PDFs: x 0 1...

Let X and Y be independent discrete random variables with the following PDFs: x 0 1 2 f(x)=P[X=x] 0.5 0.3 0.2 y 0 1 2 g(y)= P[Y=y] 0.65 0.25 0.1 (a) Show work to find the PDF h(w) = P[W=w] = (f*g)(w) (the convolution) of W = X + Y (b) Show work to find E[X], E[Y] and E[W] (note that E[W] = E[X]+E[Y])

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y is a uniform (0,6). Let W=2X-Y and Z= 2X+Y. a) Find the expected value of X, the expected value of Y, the variance of X and the variance of Y. b) Find the expected value of W. c) Find the variance of W. d) Find the covariance of Z and W. d) Find the covariance of Z and W.

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf is given as Px,y = ?(? + ? + 2)/(B + 2) for 0 ≤ X < 3, 0 ≤ Y < 3 (Where B=0) a) Find the value of ? b) Find the marginal pmf of ? and ? c) Find conditional pmf of ? given ? = 2

Let X and Y be random variables with finite means. Show that min g(x) E(Y−g(X))^2=E(Y−E(Y|X))^2 Hint:...

Let X and Y be random variables with finite means. Show that min g(x) E(Y−g(X))^2=E(Y−E(Y|X))^2 Hint: a−b = a−c+c−b

Question

Let X and Y be two discrete random variables with a common mgf of e^(4t). After...

Solutions

Expert Solution

Related Solutions

Let X and Y be two discrete random variables with a common mgf of e^(4t). After...

Let X and Y be jointly normal random variables with parameters E(X) = E(Y ) =...

Let X and Y be continuous random variables with E[X] = E[Y] = 4 and var(X)...

Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...

Let X and Y be two discrete random variables whose joint probability distribution function is given...

Let X and Y be independent discrete random variables with the following PDFs: x 0 1...

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables. X is a binomial (25,0.4) and Y...

SOLUTION REQUIRED WITH COMPLETE STEPS Let X and Y be discrete random variables, their joint pmf...

Let X and Y be random variables with finite means. Show that min g(x) E(Y−g(X))^2=E(Y−E(Y|X))^2 Hint:...