The joint density function of (X, Y) is given by c(2x + y) if 0 < x < 1, 0< y < 1, | 0 fx,Y (x, y) = otherwise. (a) Find c. (b) Derive the marginal distribution for X, i.e. fx(x). (c) Are X and Y independent? Justify your answer. (d) Compute E (Y|X = 0.1).
The joint density
2.
Suppose that cars coming off the production line at a GM factory are either have defective engines, something else that is defective, or they are not defective. Assume that each of these possibilities is equally likely for all cars that are produced. Let D1 denote a defective engine, let D2 denote a car that is defective in some other way than the engine, and let DC denote a non-defective car. No arithmetic for this problem or simplify things like (). (a) If a single car is to be selected, and the only interest in whether the car is defective in one of the two ways, or not defective, give an appropriate
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