Hello there,

I need your help for my questions please about " Covariance and Correlation"

please take a look

Exercise 13. You toss a coin n times. Let X be the number of Heads, Y = n X the number of Tails. (a) Find ]E(X), ]E(Y), Var(X) and Var(Y). (b) Find ]E(X2] (for example by using the formula ]E(X2) : Var(X) + (WW). (c) Find lE(XY). (d) Find Cov(X, Y) and p(X,Y). Exercise 13.4. Let X and Y be discrete random variables, both taking values either 1 or 2. Let their joint distribution be given by 1P(X=1,Y=1) = 1/6 1P(X=1,Y=2) = 1/4 1P(X=2,Y=1) = 1/4 1P(X=2,Y=2) = 1/3 (a) Find 1P(X = 1), P(X = 2), My = 1) and My = 2). (b) Find 1E(X) and 1130/). (c) Find Var(X) and Var(Y). (d) The random variable Z = XY takes values 1, 2 and 4. Find P(Z =1), 1P(Z = 2), 1P(Z = 4) and ]E(Z). (e) Find Cov(X, Y) and p(X, Y)