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- Consider a random variable Y that follows an exponential distribution with a rate parameter of 0.5. What is the probability that Y is greater than 2?a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? x. What is the probability that the lifetime of at least one component exceeds 3?If X is a random variable having a normal distribution with the mean μ and standard deviation σ, how do you show the moment generating function of Z=(X-μ)/σ is the moment generating function of the standard normal distribution?