Question

Suppose the Value of a raw, uncut ruby is a function of its Weight (in carats) and Diameter (in millimeters). In particular, suppose this function is V = 5+10W + 5D. As you might expect, these two variables have a positive correlation, which we'll assume is p=.75. Of all the rubies mined in a year, the distribution of W is normal with a mean of 1.5 and variance of 5. D is also normally distributed, but with a mean of 4 and variance of 1.

a. What is the expected value and variance of the Value of a randomly chosen ruby?

b. Given your answer in part a, what is the probability that a randomly chosen ruby's value is greater than 50? (Be sure to show your work here, in case you make a mistake in part a.)

Answer 1