Context: The random variables X and Y have the joint PMF: px,y(x, y)=c*(x+y)^(2) if x belongs to {1,2,4} and y belongs to {1,3} and otherwise px,y(x,y) =0. Find the expectations E[XY].

If X and Y are independent random variables with means E[X] = 2 and E[Y] = 3, what is the expected value of XY?Review LaterE[XY] = 5E[XY] = 6E[XY] = 7E[XY] = 8

The random variables X and Y have the joint PMF: px,y(x, y)=c*(x+y)^(2) if x belongs to {1,2,4} and y belongs to {1,3} and otherwise px,y(x,y) =0. Find the value of c. Find P(Y<X) and P(Y=X).

Context: if x y are two random variable then e(xy) Answer question

1. Let X and Y be two random variables with joint pmf as follows.yfX,Y (x, y) -1 1 2x-2 0.15 0.10 0.051 0.25 0.25 0.20(a) Let event A = {{X is even} ∩ {Y is odd}}. Find PA
. [2 marks](b) Find the marginal pmf’s fX (x) and fY (y). [3 marks](c) Find E(XY ). [2 marks](d) Find E(X + Y ). [2 marks](e) Are X and Y independent? Justify your answer. [1 mark](f) Let event A = {{X is even} ∩ {Y is odd}}. Compute the conditional probability massfunction fY |A(y) for Y given A occurs. [3 marks](g) Find the conditional pmf fX|Y (x|2). [2 marks](h) Find E[X|Y = 2]. [2 marks](i) Find Cov(X, Y ). [2 marks](j) Find Var(X + Y). [4 marks](k) Compute the correlation ρX,Y .

Quiz question. Random variables X and Y have joint p.m.f. shown in the following table: y fX,Y (x, y) 0 1 x 1 2 0.2 0.8 0.3 1 (a) Fill in the missing values. (b) Find P(X + Y ≤ 2). (c) Find E(XY )