Question 6, 7, 8
6. Let the random variable X have the p.d.f.
Need Help Writing an Essay?
Tell us about your assignment and we will find the best writer for your paper.
Write My Essay For Mef ( x ) =
8
2
2
1
?
x
e
?
, 0 < x < ?, zero elsewhere.
Find the mean and the variance of X.
Hint: Compute E ( X ) directly and E ( X
2
) by comparing the integral with the integral
representing the variance of a random variable that is N ( 0, 4 ).
7 – 8. (i) Give the name of the distribution of X (if it has a name), (ii) find the values
of µ and ?
2
, and (iii) calculate P ( 1 ? X ? 2 ) when the moment-generating
function of X is given by
7. a) M X ( t ) =
1 2.5 t
1
?
, t < 0.4.
b) M X ( t ) =
3
1 25.0
1
?
?
?
?
?
?
? t
, t < 4.
8. c) M X ( t ) = e
3 t + 2 t
2
.
d) M X ( t ) =
t
t
e
5
1
5
?
, t ? 0, M X ( 0 ) = 1
Welcome to one of the most trusted essay writing services with track record among students. We specialize in connecting students in need of high-quality essay writing help with skilled writers who can deliver just that. Explore the ratings of our essay writers and choose the one that best aligns with your requirements. When you rely on our online essay writing service, rest assured that you will receive a top-notch, plagiarism-free A-level paper. Our experienced professionals write each paper from scratch, carefully following your instructions. Request a paper from us and experience 100% originality.