HW10. MA3160 Fall 2021 Due November 18

Posted on December 4, 2017 by Fabrice Baudoin

Exercise. Let (X,Y) have joint density f(x,y)=c e^{-x-2y} if x,y \ge 0 and 0 otherwise.

(a)  Find c that makes this f a joint pdf.

(b) Are X and Y independent ?

(c) Compute E(XY^2)

(d) Compute Var(X+Y)

Honors exercise.

Let X_1 be a an exponential random variable with parameter one  and  let X_2 be an exponential random variable with parameter 2. We assume that X_1 and X_2 are independent. Compute the density of the random variable Z=X_1+X_2,

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