Problem 3 If the probability density function of random variable is given by ƒ(x) = echx (a)Find the mean (b)Find the total area

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Answer Problem 3 only, disregard the other problems in the picture.

Please express answers in fraction and simplified form only. thank you.

Problem 1.
A continuous random variable X is defined by
(3+x)²
16
f(x) =
- 3<xS-1
(6- 2)
16
(3-r)
16
-13x<3
(a)Verify that f(x) is density. Explain
(b)Find the Mean
Problem 2
If the probability density function of random variable is given by
f(x) = sinh 2x
(a) Find the mean
(b) Find the total area
(c) Illustrate the graph ( use Bell shaped figure)
Problem 3
If the probability density function of random variable is given by
f(x) = ech x
(a)Find the mean
(b)Find the total area
Transcribed Image Text:Problem 1. A continuous random variable X is defined by (3+x)² 16 f(x) = - 3<xS-1 (6- 2) 16 (3-r) 16 -13x<3 (a)Verify that f(x) is density. Explain (b)Find the Mean Problem 2 If the probability density function of random variable is given by f(x) = sinh 2x (a) Find the mean (b) Find the total area (c) Illustrate the graph ( use Bell shaped figure) Problem 3 If the probability density function of random variable is given by f(x) = ech x (a)Find the mean (b)Find the total area
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