PROBLEM 20E

Let X have a uniform distribution on the interval (0, 1). Given that X = x, let Y have a uniform distribution on the interval (0, x + 1).

(a) Find the joint pdf of X and Y. Sketch the region where f (x, y) > 0.

(b) Find E(Y | x), the conditional mean of Y, given that X = x. Draw this line on the region sketched in part (a).

(c) Find fY(y), the marginal pdf of Y. Be sure to include the domain.

Statistics 201 β Professor Baek Section Titles Vocab Subtitles Chapter 6: Probability Distributions Section 6.1 1. Random Variable: a numerical measurement of the outcome of a random phenomenon; randomness often results from the use of random sampling or a randomized experiment to gather the data 2. Probability Distribution: specifies its possible values and their probabilities (for random variables) 3. Probability distribution of a discrete random variable assigns a probability to each possible value a. For each x, the probability P(x) falls between 0 and 1 b. The sum of the probabilities for all the possible x values equals 1 4. The mean of a probability distribution for a discrete random variable is: