Question

Engineering Economics

3. (Total 6 points) Let (X,Y) be a pair of continuous random variables which take values on [0, 1] × [0, 1]. For some constant 0 E [0, 1], the joint cdf of Xand Y is provided by

F_{X Y}(x, y)=\frac{x y}{1-\theta(1-x)(1-y)} \text { for } 0 \leq x \leq 1 \text { and } 0 \leq y \leq 1

a) (1 point) What is P(X < 1/2and Y< 1/3})?

(b) (1 point) What is P(X >1/2 and Y <1/3 )?

(c) (2 points) What do you know about the distribution of X? And what do you know about the distribution of Y? (Hint: find the CDF of X and the CDF of Y).

(d) (2 points) Suppose that theta = 0. Calculate Corr(X,Y).