where 0 x < oo and 0> 0.e is a parameter of the exponential distribution, a fixed constant that controls the shape andvariability of the probability density function. Note that each value of e generates a distinctexponential distributionThe mean of a probability density function is referred to as its expected value. We can use theintegral to calculate the expected value, denoted E(f)E(f)xf(x)dxThe variance of a probability density function describes the variability of the distribution. Thevariance, denoted V(f), can also be calculated using the integralv) Ef2)-E)

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Asked Nov 26, 2019
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How are the mean and variance of an exponential random variable related? *requires integration by parts? More information is given in the picture but this is the question i am trying to answer. I really would appreciate clean handwriting in the answer as a lot of answers and variables are too difficult for me to follow

where 0 x < oo and 0> 0.
e is a parameter of the exponential distribution, a fixed constant that controls the shape and
variability of the probability density function. Note that each value of e generates a distinct
exponential distribution
The mean of a probability density function is referred to as its expected value. We can use the
integral to calculate the expected value, denoted E(f)
E(f)xf(x)dx
The variance of a probability density function describes the variability of the distribution. The
variance, denoted V(f), can also be calculated using the integral
v) Ef2)-E)
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where 0 x < oo and 0> 0. e is a parameter of the exponential distribution, a fixed constant that controls the shape and variability of the probability density function. Note that each value of e generates a distinct exponential distribution The mean of a probability density function is referred to as its expected value. We can use the integral to calculate the expected value, denoted E(f) E(f)xf(x)dx The variance of a probability density function describes the variability of the distribution. The variance, denoted V(f), can also be calculated using the integral v) Ef2)-E)

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Expert Answer

Step 1

Introduction:

For any continuous random variable, X with probability density function f (x), the expectation, E...

E (x)=(x)dx
V(x)E(x2)-[E(x)
-frf(x)dx-xf(x) d.
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E (x)=(x)dx V(x)E(x2)-[E(x) -frf(x)dx-xf(x) d.

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