Question: 4. Let X and Y have the joint density function. f(x, y) = Se-(x+y), x>0, y> 0 0, elsewhere (a) Show that this is

4. Let X and Y have the joint density function. f(x, y) = Se-(x+y), x>0, y> 0 0, elsewhere (a) Show that this is a probability density function. (b) What is the probability that X > 1 and Y < 4? (c) What is P(Y X)? (d) Find the marginal density functions for X and Y. Classify the random variables X and Y according to their distributions. What type of random variables are they? (e) Find f(xy). (f) An analyst claims that the random variables X and Y are independent. Is this a reasonable claim? Be sure to show mathematically how you made your conclusion.

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