Let X and Y be independent random variables. X is N(1,9) and Y is uniform on the interval {-1, 1]. La Write down the joint density for (X,Y) d Give the mean and variance of Y c) Give the median of X I Y Give the correlation coefficient p of X and Y

We expect poorer countries (X=1) to grow faster (Y=1) than richer countries-the table below displays countries' relative incomes and growth rates. Poorer than average (X=1) Richer than average (X=0) Ten-year growth above Ten-year growth below average (Y=1) average (Y=0) 0.38 0.14 0.13 a) Find the covariance between the two variables. 0.35 b) Interpret in plain words the independence between X and Y. (up to 40 words)

The random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y,    for 0<x<1, 0<y<1                   0,              otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y?  (d) What is the correlation of X and Y?

Let U1, U2, U3, .,U60 be independent and identically distributed U;~Unif(0,1) and X = U, + U2 + U3 + …+ U60. Which of these distributions approximates the distribution of X? Select one: N(30,5) Bin(30,0.5) Bin(60,0.5) N(0,1)