Each front tire ona vehicle is supposed to be filled to a pressure of 16 psi. Suppose the actual airpressure in each tire is a random variable. X for the right tire and Y for the left tire, with a joint pdf a) Find the value of k that makes this a valid probability density function. b) Are X and Y independent randome variables? c) What is the probability that both tires are underfilled? d) Determine the marginal distribution of the right tire. e) Determine the conditional probability density function of Y given X=x.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7