statistics , calculus and probability questions - need help

Question 12 3 pts Suppose that X is a random variable with a mean of 6 and variance of 8; Y is a random variable with a mean of -10 and variance of 18; and Cov(X, Y) = -8. Find Corr( X, Y). O -1/3 O -1/2 O -2/3 O -3/4 O -4/5 Question 13 3 pts Given an exponential random variable X ~ Exp(X = 1/180), what is the conditional probability P(X > 100/X > 40)? O e-1/3 O e-2/9 O e-1/9 O e-1/18 01-e 2/9If X1, X2, ..., X100 are i.i.d. Nor(300, 500), then what is the distribution of the sample mean X? O Nor (3, 0.05) O Nor (3, 5) O Nor (3, 500) O Nor(300, 0.05) O Nor(300, 5) Question 16 3 pts Suppose X1, . . ., X100 are i.i.d. from an Exp(1) distribution. If we use the Central Limit Theorem approximation, what is P ( _, , X;