Question

A​ salesperson's monthly expenses​ (in thousands of​ dollars) are exponentially​ distributed, with an average of 2.75 ​(thousand dollars). A. Give the probability density function for the expenses. B. Find the probability that the expenses are more than ​$4​,000.

Answer 1

Explanation:

Given that a salesperson's monthly expenses​ (in thousands of​ dollars) are exponentially​ distributed, with an average of 2.75 ​(thousand dollars).

Hence pdf of X is

a)
`f(x) = (1)/(2,75) e^{(-x)/(2.75) } \\f(x) = 0.3636e^(-0.3636t) ,t\geq 0`

b)
`P(X\geq 4000) = e^(-0.3636*4000) \\=0.00000\\`

Almost negligible.