Question

Problem 1. This joint pdf appeared in Section 2, Example 8.2.1. Gasoline is to be stocked in a bulk tank once each

week and then sold to customers. Let X denote the proportion of the tank that is stocked in a particular week, and let

Y denote the proportion of the tank that is sold in the same week. Due to limited supplies, X is not fixed in advance

but varies from week to week. Suppose that a study of many weeks shows the joint relative frequency behavior of X

and Y to be such that the join density function provides and adequate model:

f(x,y)=3x,  0<=y<=x<=1 (<= means less than or equal to)

(e) Compare the marginal expectation of X with the marginal expectation of X when Y=0.4.

(f) Calculate the covariance between X, Y?

Answer 1