Exercise 1

Suppose that X is exponentially distributed with parameter ) = 3. Given that X=x, Y is normally distributed with mean 0 and standard deviation x. Which of the following is the conditional probability density of Y given X=x? 1. (3/2)2 V2T C e 2 V2 Ty e 2 3 e-3x (y/x)2 V2 TC e 2 3 e- 3x (3/y)2 V2 TT y e 2Step 1. You roll a six-sided die. Let X be the (random) number that you obtain. Step 2. You roll X six-sided dice. Let Y be the total number (sum) that you obtain from these X dice. Find EY , rounded to nearest .xx.Suppose that random variables X and Y are independent. Further, X is a normal random variable with mean = 3 and standard deviation g = 4, and Y is an uniformly distributed random variable on the interval (0, 5). Find the correlation between X and Y, rounded to nearest .xx