Question

Problem 4. Exercise 11, p.296, Section 8.12 Textbook (From Page 1989, 134.) In a certain device, X represents the voltage drop across a component and Y represents the current in another part of the device. The two are related probabilistically, however. Let?s suppose that X and Y have a joint density function

f(x, y) = c

in the part of the first quadrant bounded by the curve y = 4 − x 2 and the x axis, with f(x,y)=0 outside this region.

(a) Find the value c must have to make this a joint density

(b) Find the marginal densities of X and Y.

(c) What is the probability that 3X is greater than Y? Draw the region of the plane where you will have to integrate the joint density to find this probability.

Answer 1