Question find mean and variance ,MGF of one random variable derive that step by step for number 2,3,4.Thank you

3: Hence, MGF is Differentiating with respect to t gives: The mean is: Differentiating with respect to t again gives: So, The variance is: 4:

Here we will use the intergral -----------

PDF of gamma distribution with parameter and is Let us assume .

So pdf of gamma distribution will be So MGF will be    So MGF is Now putting gives ----------------

Differentiating MGF with respect to t once gives: Noe putting t=0 in the above equation gives: Differentiating MGF with respect to t again gives: Noe putting t=0 in the above equation gives: Now putting gives Therefore variance is: #### Earn Coins

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