Question

Find the following probabilities if the joint probability density function of 𝑋 and 𝑌 is

given by

𝑓(𝑥, 𝑦) = {

2𝑒

−𝑥𝑒

−2𝑦

if 0 < 𝑥 < ∞, 0 < 𝑦 < ∞

0 otherwise

a. 𝑃(𝑋 > 1, 𝑌 < 1)

b. 𝑃(𝑋 < 𝑌)

c. 𝑃(𝑋 < 𝑎)