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

Rui Baldwin

Rui Baldwin

Answered question

2021-06-03

Find the expected values and variances of the exponential random variables with the density functions given below
14ex4

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-06-04Added 93 answers

Step 1
it is given that x is a exponential random variables with pdf,
f(x)=14ex4
Step 2
Pdf of exponential distribution
f(x)=0e0x,x0
Mean of exponential distribution =10
Variance of exponential distribution =102
Given pdf, f(x)=14ex4
Comparing it with pdf of exponential distribution, 0=14
Mean of exponential distribution =114=4
Variance of exponential distribution =1(14)2=16

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