a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find itsmoment generating function272b) The random variable X has the following moments: E(X")n =1,2,... .n1Find the moment generating function of X and identify the distribution of X. Hint: Usethe Taylor expansion of etX to find the moment generating function, and use problem a)to identify the distribution

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Asked Nov 9, 2019

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a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find its
moment generating function
272
b) The random variable X has the following moments: E(X")
n =1,2,... .
n1
Find the moment generating function of X and identify the distribution of X. Hint: Use
the Taylor expansion of etX to find the moment generating function, and use problem a)
to identify the distribution
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a) Let Xbe a random variable with uniform distribution on the interval (a, b). Find its moment generating function 272 b) The random variable X has the following moments: E(X") n =1,2,... . n1 Find the moment generating function of X and identify the distribution of X. Hint: Use the Taylor expansion of etX to find the moment generating function, and use problem a) to identify the distribution

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Step 1

As you have posted 2 different questions, we are answering the first question. In case you require the unanswered questions also, kindly re-post them as separate questions.

Step 2

a)

 

From the given information, the random variable X follows uniform distribution on interval

(a, b).

 

The probability density function for X is,

1
-,asX<b
b- a
f(x)
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1 -,asX<b b- a f(x)

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Step 3

The moment generating...

Mx (t)E(e)
b
-fe f(x)c
a
1
b-a
a
b
1
e d
b-a
1
b-a
1 e
e'a
b-a
eb -ea
(b-a)
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Mx (t)E(e) b -fe f(x)c a 1 b-a a b 1 e d b-a 1 b-a 1 e e'a b-a eb -ea (b-a)

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