Question

Find the expected values and variances of the exponential random variables with the density functions given below \frac{1}{4}e^{-\frac{x}{4}}

Random variables
ANSWERED
asked 2021-06-03
Find the expected values and variances of the exponential random variables with the density functions given below
\(\frac{1}{4}e^{-\frac{x}{4}}\)

Answers (1)

2021-06-04
Step 1
it is given that x is a exponential random variables with pdf,
\(f(x)=\frac{1}{4}e^{-\frac{x}{4}}\)
Step 2
Pdf of exponential distribution
\(f(x)=0e^{-0x}, x\geq 0\)
Mean of exponential distribution \(= \frac{1}{0}\)
Variance of exponential distribution \(= \frac{1}{0^{2}}\)
Given pdf, \(f(x)=\frac{1}{4}e^{-\frac{x}{4}}\)
Comparing it with pdf of exponential distribution, \(0 =\frac{1}{4}\)
Mean of exponential distribution \(= \frac{1}{\frac{1}{4}}=4\)
Variance of exponential distribution \(= \frac{1}{(\frac{1}{4})^{2}}=16\)
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