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

Answer:

Step-by-step 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) $f(x) = \frac{1}{2,75} e^{\frac{-x}{2.75} } \\f(x) = 0.3636e^{-0.3636t} ,t\geq 0$

b)  $P(X\geq 4000) = e^{-0.3636*4000} \\=0.00000$

Almost negligible.