Question

The random variable X has moment generating function

ϕX(t)=exp((9t)^2)/2)+15t)

Provide answers to the following to two decimal places

(a) Evaluate the natural logarithm of the moment generating
function of 2X at the point t=0.62.

(b) Hence (or otherwise) find the expectation of 2X.

c) Evaluate the natural logarithm of the moment generating function of 2X+7 at the point t=0.62.

Answer #1

a)

MGF of X:

So, MGF of 2X is given by:

So,

Required value =

b)

Now,

We know that,

So,

c)

The MGF of 2X+7 is given by:

So,

Required value =

The random variable X has moment generating function
ϕX(t)=(0.44e^t+1−0.44)^8
Provide answers to the following to two decimal places
(a) Evaluate the natural logarithm of the moment generating
function of 3X at the point t=0.4.
(b) Hence (or otherwise) find the expectation of 3X.
(c) Evaluate the natural logarithm of the moment generating
function of 3X+6 at the point t=0.4.

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Suppose that the moment generating function of a random variable
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Find E[X]. Find E[Z ]. Compute E[X] another way - try to recognize
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Suppose that a random variable X has the following
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M X (t) = (1 −
3t)−8, t < 1/3. (a)
Find the mean of X (b) Find the Varience of X. Please explain
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(i) If a discrete random variable X has a moment generating
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Find the probability mass function of X. (ii) Let X and Y be two
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Let ? and ? be two independent random variables with moment
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