Solution Found!
There are times when a shifted exponential model is
Chapter 3, Problem 5E(choose chapter or problem)
There are times when a shifted exponential model is appropriate. That is, let the pdf of \(X\) be
\(f(x)=\frac{1}{\theta} e^{-(x-\delta) / \theta}, \quad \delta<x<\infty\)
(a) Define the cdf of \(X\).
(b) Calculate the mean and variance of \(X\).
Equation Transcription:
Text Transcription:
X
f(x)=1/theta e^-(x-delta)/theta, delta <x<infinity
Questions & Answers
QUESTION:
There are times when a shifted exponential model is appropriate. That is, let the pdf of \(X\) be
\(f(x)=\frac{1}{\theta} e^{-(x-\delta) / \theta}, \quad \delta<x<\infty\)
(a) Define the cdf of \(X\).
(b) Calculate the mean and variance of \(X\).
Equation Transcription:
Text Transcription:
X
f(x)=1/theta e^-(x-delta)/theta, delta <x<infinity
ANSWER:Solution 5E
Step1 of 3:
We have A Exponential random variable X with pdf
We need to find,
(a) Define the cdf of X.
(b) Calculate the mean and variance of X.
Step2 of 3:
Let “X” be random variable which follows Exponential distribution with parameters .
That is X Exp(
)
The probability mass function of binomial distribution is given below
Where,
X = random variable
= parameter
= parameter
e = a constant it is approximately 2.7182.
a).
Consider,
To get a cdf of X we need to integrate above function with respect to x.
1).If X < then,
=
= 0.
2).If X then,