Suppose that X is uniform distributed on [1,b] with E(X)=5. (1) Find the upper bound b. (2) What is Var(X) (3) P(X<3) (4) P(X>5) please explain with all the steps
Suppose that X is uniform distributed on [1,b] with E(X)=5. (1) Find the upper bound b. (2) What is Var(X) (3) P(X<3) (4) P(X>5) please explain with all the steps
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that X is uniform distributed on [1,b] with E(X)=5. (1) Find the upper bound b.
(2) What is Var(X)
(3) P(X<3)
(4) P(X>5)
please explain with all the steps
Expert Solution

Step 1
Introduction:
A uniform distribution, also called a rectangular distribution, is a probability distribution that has constant probability.
This distribution is defined by two parameters, a and b:
- a is the minimum.
- b is the maximum.
The general formula for the probability density function (pdf) for the uniform distribution is:
f(x) = 1/ (B-A) for A≤ x ≤B.
Where “A” is the location parameter The location parameter tells you where the center of the graph is. “B” is the scale parameter. The scale parameter stretches the graph out on the horizontal axis.
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