#1. Suppose that X and Y have joint pdf: f(x,y)= (2x+y)/2,0

Suppose that X and Y have joint pdf: f(x,y)= f(x,y)=0,elsewhere. (a)Find the mean and variance of X. (b)Find the mean and variance of Y. (c)Find the covariance of X and Y. (d)Find the correlation coefficient of X and Y. (d) Let w(x) = exp(-x). Verify that Jensen's inequality holds, that is, verify that Let X be a random variable with: Find the mean and variance of X. Toss a coin 25 times. Find the probability that the number of heads falls between 10 and 15 (inclusive): (a)using the appropriate exact distribution (b)using the normal approximation to the distribution in (a). Compare to the answer in (a).