Stat 400 In Class Worksheet 4
T.A. Emily King
February 27, 2008
1. (Book p 107 #33) Let Xbe a Bernoulli rv with pmf as in Example 3.18.
(a) Compute E(X2).
(b) Show that V(X) = p(1 −p).
(c) Compute E(X79).
2. (Book p 107 #34) Suppose that the number of plants of a particular type
found in a rectangular region in a certain geographic area is an rv X with
pmf
p(x) =
c/x3x= 1,2,3, . . .
0 otherwise
Is E(X) finite? Justify your answer.
3. (Book p 107 #42) Suppose E(X) = 5 and E[X(X−1)] = 27.5. What is
E(X2)? V(X)?
4. (Book p 115 #59ab) An ordinance requiring that a smoke detector be
installed in all previously constructed houses has been in effect in a par-
ticular city for 1 year. The fire department is concerned that many houses
remain without detectors. Let p= the true proportion of such houses hav-
ing detectors, and suppose that a random sample of 25 homes is inspected.
If the sample strongly indicates that fewer than 80% of all homes have a
detector, the fire department will campaign for a mandatory inspection
program. Because of the costliness of the program, the department prefers
not to call for such an inspection unless sample evidence strongly argues
for their necessity. Let Xdenote the number of homes with detectors
among the 25 sampled. Consider rejecting the claim that p≥.8 if x≤15.
