Question

1-1.2 In determining the probability characteristics of printed English, it is common to consider a 27-letter alphabet in which the space between words is counted as a letter Punctuation is usually ignored. a) Count the number of times each of the 27 letters appears in this problem. b) On the basis of this count, deduce the most probable letter, the next most probable letter, and the least probable letter (or letters). 1-2.1 For each of the following random experiments, list all of the possible outcomes and state whether these outcomes are equally likely. a) Flipping two coins. b) Observing the last digit of a telephone number selected at random from the directory. c) Observing the sum of the last two digits of a telephone number selected at random from the directory.

Answer 1

1-2.1

a)

When we flip a coin possible outcomes are head(H) and tail (T). The possible number of outcomes when 2 coins are tossed is 2*2 = 4

The sample space is:

$S=\left \{ HH,HT,TH,TT \right \}$

All of these outcomes are equally likely.

b)

There are 10 possible digits. The last digit can be one of these 10 digtis. All these digits are equally likely and possible sample space is:

S = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

c)

The last two digtis can be selected in 10*10 = 100 ways

The sum of digtis can take values between 0 and 18. Following table shows the possible sum of probabilites:

Sum, X	P(X=x)
0	0.01
1	0.02
2	0.03
3	0.04
4	0.05
5	0.06
6	0.07
7	0.08
8	0.09
9	0.1
10	0.09
11	0.08
12	0.07
13	0.06
14	0.05
15	0.04
16	0.03
17	0.02
18	0.01

These values are not equally likely.