Let y1 and y2 have the joint probability density function given by f (y1, y2) = ( k*y1*y2), 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1, 0, elsewhere. a find the value of k that makes this a probability density function. b find the joint distribution function for y1 and y2.

k = 4

F(y1,y2) = y1²y2²

Step-by-step explanation:

We have to integrate that expression over the domain given and find k so that the integral is equal to 1. The integral can be computed by applying Barrow's Rule twice.

In order for this integral to be equal to 1 we need that k/4 = 1, hence k=4.

The joint distribution function is obtained from the computation we made above, replacing k by 4 before applying Barrow's Rule.

1,918

step-by-step explanation: