Question

2. Suppose the mgf of a discrete random variable X is $M_X(t) = \frac{1}{4}e^{-2t} + \frac{1}{4}e^{-t} + \frac{1}{8}e^{2t} + \frac{3}{8}e^{5t}$ (a) Find the expectation E(X) (b) Find the expectation E(X$^2$) (c) Find the expectation E(X$^2$ - 3X + 4) (d) Write down the pmf of X

          2. Suppose the mgf of a discrete random variable X is $M_X(t) = \frac{1}{4}e^{-2t} + \frac{1}{4}e^{-t} + \frac{1}{8}e^{2t} + \frac{3}{8}e^{5t}$
(a) Find the expectation E(X)
(b) Find the expectation E(X$^2$)
(c) Find the expectation E(X$^2$ - 3X + 4)
(d) Write down the pmf of X

2. Suppose the mgf of a discrete random variable X is MX(t) = (1)/(4)e^-2t + (1)/(4)e^-t + (1)/(8)e^2t + (3)/(8)e^5t
(a) Find the expectation E(X)
(b) Find the expectation E(X^2)
(c) Find the expectation E(X^2 - 3X + 4)
(d) Write down the pmf of X

Added by Kristie M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

05/14/2022

Step 1

Step 1: The mgf of a discrete random variable X is given by: $M_X(t) = E(e^{tX})$ Show more…

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2. Suppose the mgf of a discrete random variable X is $M_X(t) = \frac{1}{4}e^{-2t} + \frac{1}{4}e^{-t} + \frac{1}{8}e^{2t} + \frac{3}{8}e^{5t}$ (a) Find the expectation E(X) (b) Find the expectation E(X^2) (c) Find the expectation E(X^2 - 3X + 4) (d) Write down the pmf of X