Suppose that actual air pressure in each front tire of a vehicle where X is a random variable for the right tire and Y for the left has a joint pdf as

F(x,y) = K(x²+y²) where 20 < x < 30 , 20 < y < 30

a. Determine the conditional pdf of Y given that X = x and the conditional pdf of X given that Y = y

b. If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi?

c. What is the probability that the left tire pressure is at least 25 psi?

Hint: Take a look at the Example Continuous Joint Probability Distribution Problem Video 3 within Week 8 Learning Module as this problem is related to that example and it also solves for K that you can use in this problem