Question

Let x denote the time (in minutes) that a person spends waiting in a checkout line at a grocery store and y the time (in minutes) that it takes to check out. suppose the joint probability density for x and y is f(x, y) = 1 8 e −x/4e −y/2 . what is the exact probability that a person spends between 0 to 5 minutes waiting in line, and then 0 to 5 minutes waiting to check out

Answer 1

To find the exact probability that a person spends between 0 to 5 minutes waiting in line, and then 0 to 5 minutes waiting to check out, we need to integrate the joint probability density function over the given range.

Step-by-step explanation:

To find the probability that a person spends between 0 to 5 minutes waiting in line, and then 0 to 5 minutes waiting to check out, we need to integrate the joint probability density function over the given range.

The joint probability density function is given as f(x, y) = (1/8)e^(-x/4)e^(-y/2). To find the exact probability, we integrate this function over the given range:

Probability = ∫(from 0 to 5) ∫(from 0 to 5) (1/8)e^(-x/4)e^(-y/2) dx dy.

Integrating this expression will give us the exact probability.