Question

3. The following three questions will assume the same joint distribution of X and Y as described here. Let X and Y each take on either values 1 or -1. Let p(x,y) represent P\{X = x, Y = y\}. Suppose E[X] = E[Y] = 0. show that p(1, 1) = p(-1, -1). Hint: if Z = X + Y, note that E[Z] = 0 and compute the expectation of Z with the joint mass function of X, Y. 4. Show that p(-1,1) = p(1,-1) 5. Compute Var(X) and Var(Y)

          3. The following three questions will assume the same joint distribution of X and Y as described here. Let X and Y each take on either values 1 or -1. Let p(x,y) represent P\{X = x, Y = y\}. Suppose E[X] = E[Y] = 0. show that p(1, 1) = p(-1, -1).
Hint: if Z = X + Y, note that E[Z] = 0 and compute the expectation of Z with the joint mass function of X, Y.
4. Show that p(-1,1) = p(1,-1)
5. Compute Var(X) and Var(Y)

3. The following three questions will assume the same joint distribution of X and Y as described here. Let X and Y each take on either values 1 or -1. Let p(x,y) represent P{X = x, Y = y}. Suppose E[X] = E[Y] = 0. show that p(1, 1) = p(-1, -1).
Hint: if Z = X + Y, note that E[Z] = 0 and compute the expectation of Z with the joint mass function of X, Y.
4. Show that p(-1,1) = p(1,-1)
5. Compute Var(X) and Var(Y)

Added by Joan F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/28/2023

Step 1

Let Z = X + Y. Therefore, E[Z] = 0. Show more…

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The following three questions will assume the same joint distribution of X and Y as described here. Let X and Y each take on either values 1 or -1. Let p(x,y) represent P{X=x,Y=y}. Suppose E[X]=E[Y]=0. Show that p(1,1)=p(-1,-1). Hint: if Z=X+Y, note that E[Z]=0 and compute the expectation of Z with the joint mass function of X,Y. Show that p(-1,1)=p(1,-1). Compute Var(X) and Var(Y).