Probability and Statistics
1. The price-to-earnings (PE) ratio of a stock is the ratio of a stock's most recent price per share to the stock's earnings per share (averaged over a 12-month period). Listed below are the PE ratios for 40 randomly selected securities traded on the New York Stock Exchange (NYSE) on Wednesday, August 24, 2005.
|
Stock
|
PE Ratio
|
|
1
|
ALLGWASTE
|
25
|
|
2
|
AZISTA
|
22 |
|
3
|
CIMAREXENGY
|
10
|
|
4
|
DEVRY
|
47
|
|
5
|
DLRGENL
|
18
|
|
6
|
ENPRO
|
15
|
|
7
|
GENESCO
|
18
|
|
8
|
GILDAN
|
27
|
|
9
|
GUESS
|
26
|
|
10
|
HEAD
|
33
|
|
11
|
HOSPIRA
|
23
|
|
12
|
IBM
|
17
|
|
13
|
INCO
|
10
|
|
14
|
JEFFPILOT
|
12
|
|
15
|
K2
|
25
|
|
16
|
KINDRED
|
10
|
|
17
|
LEAR
|
15
|
|
18
|
MANPOWER
|
17
|
|
19
|
MESTEK
|
4
|
|
20
|
MIHOMES
|
10
|
|
21
|
MYLANLABS
|
30
|
|
22
|
NUCOR
|
6
|
|
23
|
ONEOK
|
14
|
|
24
|
PROQUEST
|
22
|
|
25
|
PULTE
|
9
|
|
26
|
RUDDICK
|
16
|
|
27
|
SIRVA
|
40
|
|
28
|
STEINWAY
|
15
|
|
29
|
TESORO
|
13
|
|
30
|
TORCHMARK
|
12
|
|
31
|
TORO
|
16
|
|
32
|
UNITCP
|
18
|
|
33
|
VARIANMED
|
27
|
|
34
|
WALLGREEN
|
31
|
|
35
|
WELLCHOICE
|
22
|
|
36
|
WELLPOINT
|
23
|
|
37
|
WILEYA
|
32
|
|
38
|
XEROX
|
13
|
|
39
|
YANKEECANDL
|
16
|
|
40
|
ZIMMER
|
29
|
2. Mary tosses a coin three times and then John does the same.
a. Find the probability that Mary obtains exactly one Head.
b. Find the probability that Mary obtains exactly one Head and so does John. [Hint: We assume that Mary's tosses are completely independent from John's.]
c. Find the probability that each of them obtain exactly 2 Heads. [Hint: This means find the probability that Mary obtains 2 heads and so does John.]
d. Find the probability that each of them obtains no Heads.
e. Find the probability that they obtain the same number of Heads.
a) Give the mean variance (s2), and standard deviation (s) for this data sample.
(b) For this data sample, approximately what percentage of the data lies within one standard deviation of the mean?
(c) Create a Histogram for this data. (Use about 6 classes)