Let X and Y be two discrete random variables with a common mgf of e^(4t). After...

Let X and Y be two discrete random variables with a common mgf of e^(4t). After some analysis you conclude, X = 4 and Y = 6. Is this a valid claim? Why or why not?

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Expert Solution

Let X and Y be two discrete random variables with a common mgf of . After some analysis we conclude, X = 4 and Y = 6.

=> Our claim is invalid.

Explanation:-

[ Formula for mgf:-

For a discrete random variable M, mgf of M is given by,

]

Now if X = 4, then mgf of 4 is given by,

and given that X = 4 has mgf .

So, by the question we get,

.................(1)

Now if X = 6, then mgf of 6 is given by,

and given that X = 6 has mgf .

So, by the question we get,

..................(2)

Now since, so the values of these two cannot be equal. i.e equation (1) and equation (2) can not satisfied simultaneously.

Answer:- This proof that our claim is invalid.

orchestra answered 1 year ago

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