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 sample space and determine a probability to each sample point. (b) Suppose that a car was randomly selected from this GM factory, what is the probability that it is defective? Now suppose that 8 cars have been produced by GM factory. (c) Give a description of the appropriate sample space, then use counting methods to count the number of elements of this sample space. (d) What is the probability that 8 cars are not defective? (e) What is the probability of at least two defectives out of the 8 cars? (f) What is the probability of exactly 3 cars with defective engines and exactly 2 completely non-defective cars (so implicitly there must be 3 cars that are defective in some other way).
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
