Question

if x follows exponential distribution with mean a then its variance is equal to​

Answer 1

SOLUTION

GIVEN

X follows exponential distribution with mean a

TO DETERMINE

The variance

EVALUATION

The probability density function is given by

$\sf{ f_x(x | \lambda ) }= \begin{cases} & \sf{ \: \: \: \: \lambda {e}^{ -\lambda x } \: \: \: when \: x > 0} \\ \\ & \sf{ \: \: \: \: \: \: \: 0 \: \: \: \: \: when \: x \leqslant 0} \end{cases}$

Then we know that

$\displaystyle \sf{Mean = \frac{1}{\lambda} }$

$\displaystyle \sf{ Variance = \frac{1}{{\lambda}^{2} } }$

It is given that mean = a

So by the given condition

$\displaystyle \sf{ \frac{1}{\lambda} = a}$

Thus variance

$\displaystyle \sf{ = \frac{1}{{\lambda}^{2} } }$

$\displaystyle \sf{ = \bigg({ \frac{1}{\lambda} \bigg)}^{2} }$

$\displaystyle \sf{ = {a}^{2} }$

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Answer 2

Answer:

Step-by-ccstep explanation: