Question

Q7. Let \( X \) represent the number of policies sold by an agent in a day. The moment generating function of \( X \) is \[ M(t)=0.45 e^{t}+0.35 e^{2 t}+0.15 e^{3 t}+0.05 e^{4 t}, \text { for }-\infty<t<\infty . \] Calculate the standard deviation of \( X \).

          Q7. Let \( X \) represent the number of policies sold by an agent in a day. The moment generating function of \( X \) is
\[
M(t)=0.45 e^{t}+0.35 e^{2 t}+0.15 e^{3 t}+0.05 e^{4 t}, \text { for }-\infty<t<\infty .
\]

Calculate the standard deviation of \( X \).

Q7. Let X represent the number of policies sold by an agent in a day. The moment generating function of X is

M(t)=0.45 e^t+0.35 e^2 t+0.15 e^3 t+0.05 e^4 t, for -∞<t<∞ .

Calculate the standard deviation of X.

Added by Christopher F.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

07/28/2023

Step 1

The MGF of a random variable \( X \), \( M(t) \), is given by \( M(t) = E(e^{tX}) \). For the given MGF \( M(t) = 0.45 e^t + 0.35 e^{2t} + 0.15 e^{3t} + 0.05 e^{4t} \), we can interpret this as \( X \) being a discrete random variable taking values 1, 2, 3, and 4 Show more…

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Q7. Let \( X \) represent the number of policies sold by an agent in a day. The moment generating function of \( X \) is \[ M(t)=0.45 e^{t}+0.35 e^{2 t}+0.15 e^{3 t}+0.05 e^{4 t}, \text { for }-\infty<t<\infty . \] Calculate the standard deviation of \( X \).