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
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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
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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:
find mean and variance ,MGF of one random variable derive that step by step for number...
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