I need help solving these problems. Please help me by answering and showing explanations.

Question 3 1 pts When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment and Y represent the number of defective res. It is given that X and Y are independent with marginal PMF as shown below: a: PX ($)HyPY (y) 0 0.5 H0 0.6 1 03 H1 01 2 0.2 H2 0.05 _ H3005 H4 0.2 What is the probabilityP (X g 1 and Y 5 1)? O 0.8 O 0.56 O 0.3 o 0.33 Question 4 1 pts You have two lightbulbs of a particular lamp. Let X be the lifetime of the rst bulb and Y be the lifetime of the second bulb (in units of 10"4 hours). Suppose that X and Y are independent and each has exponential distribution with parameter A I 1. Which of the following shows the joint PDF of X and Y (a: 2 O, y 2 0)? O f(a:,y) = 1 i e_\"' 7 6? + (ff3' O 1' (92,3!) = 8'\"? O 1' (92,3!) = 8H; O ay) = 6'3 + 6'\