Solution Found!
If the moment-generating function of X is M(t) =exp(166t +
Chapter 3, Problem 6E(choose chapter or problem)
If the moment-generating function of \(X\) is \(M(t)=\) \(\exp \left(166 t+200 t^{2}\right)\), find
(a) The mean of \(X\).
(b) The variance of \(X\).
(c) \(P(170<X<200)\).
(d) \(P(148 \leq X \leq 172)\).
Equation Transcription:
Text Transcription:
X
M(t)=
(166t+200t^2)
P(170<X<200)
P(148 < or = X < or = 172)
Questions & Answers
QUESTION:
If the moment-generating function of \(X\) is \(M(t)=\) \(\exp \left(166 t+200 t^{2}\right)\), find
(a) The mean of \(X\).
(b) The variance of \(X\).
(c) \(P(170<X<200)\).
(d) \(P(148 \leq X \leq 172)\).
Equation Transcription:
Text Transcription:
X
M(t)=
(166t+200t^2)
P(170<X<200)
P(148 < or = X < or = 172)
ANSWER:
Solution 6E
Step1 of 3:
We have moment generating function of X is
We need to find,
a).The mean of X
b).The variance X
c).
d).
Step2 of 3:
Let “X” be random variable which follows normal distribution with parameters .
That is X N(
)
X N[
]
The probability mass function of normal distribution is given by
,
Where,
= mean of X
= variance
= standard deviation.
a).
As we said X be random variable which follows normal distribution with parameters .
That is X N(
)