2.5.12.) The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density func- tion given by f(x) ae-(1/5) x>0 0, elsewhere. Find (a) The value of a that makes f(x)a probability density function. (b) The probability that this individual will talk (1) between 8 and 12 minutes, (2) less than 8 minutes, (3) more than 12 minutes. (c) Find the cumulative distribution function, F(x).

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
2.5.12.) The length of time that an individual talks on a long-distance telephone call has been found to be of a random
nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density func-
tion given by
f(x) = {
ae-(1/5)x
0,
x>0
elsewhere.
Find
(a) The value of a that makes f(x)a probability density function.
(b) The probability that this individual will talk (1) between 8 and 12 minutes, (2) less than 8 minutes, (3) more
than 12 minutes.
(c) Find the cumulative distribution function, F(x).
Transcribed Image Text:2.5.12.) The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density func- tion given by f(x) = { ae-(1/5)x 0, x>0 elsewhere. Find (a) The value of a that makes f(x)a probability density function. (b) The probability that this individual will talk (1) between 8 and 12 minutes, (2) less than 8 minutes, (3) more than 12 minutes. (c) Find the cumulative distribution function, F(x).
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON