Question

4. Suppose that the MGF of a random variable X is of the form M(t) = 1/8 e^{2t} + 3/8 e^{-2t} + 1/2 e^t, -? < t < ?. (a) Using the above MGF, derive the mean of X. (b) Using the uniqueness of the MGF, derive the probability distribution of X. Hint: Think of a discrete random variable that would have this particular MGF. Then, derive P(X < 1.5).

          4. Suppose that the MGF of a random variable X is of the form

M(t) = 1/8 e^{2t} + 3/8 e^{-2t} + 1/2 e^t, -? < t < ?.

(a) Using the above MGF, derive the mean of X.

(b) Using the uniqueness of the MGF, derive the probability distribution of X. Hint: Think of a discrete random variable that would have this particular MGF. Then, derive P(X < 1.5).

4. Suppose that the MGF of a random variable X is of the form

M(t) = 1/8 e^2t + 3/8 e^-2t + 1/2 e^t, -? < t < ?.

(a) Using the above MGF, derive the mean of X.

(b) Using the uniqueness of the MGF, derive the probability distribution of X. Hint: Think of a discrete random variable that would have this particular MGF. Then, derive P(X < 1.5).

Added by Amanda C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/20/2022

Step 1

875\) ** Show more…

Show all steps

Thanks for your feedback!

4. Suppose that the MGF of a random variable X is of the form M(t) = 1/8e^{2t} + 3/8e^{-2t} + 1/2e^{t}, -infinity < t < infinity. (a) Using the above MGF, derive the mean of X. (b) Using the uniqueness of the MGF, derive the probability distribution of X. Hint: Think of a discrete random variable that would have this particular MGF. Then, derive P(X < 1.5).