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6. Using moment-generating functions, show that as α-> oo the gamma distri-bution with parameters a and 2, properly standardized, tends to the standarodnormal distribution.

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6. Using moment-generating functions, show that as α-> oo the gamma distri-
bution with parameters a and 2, properly standardized, tends to the standarod
normal distribution.
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6. Using moment-generating functions, show that as α-> oo the gamma distri- bution with parameters a and 2, properly standardized, tends to the standarod normal distribution.

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Step 1

Let X be the random variable, which follows gamma distribution.

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Step 2

The variable X is standardised as below:

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Step 3

Now, the MGF of Y can be foun...

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