Question

2.50 Consider the following message: FORMULA FOR SUCCESS (a) Estimate the probabilities of the letters in the message using the relative frequency approach. (b) Find the average information in the message.

Answer 1

Part a: The probability of each letter is given in the table below.

Part b: The average information in this message is 1.91.

Step-by-step explanation:

Part a:

The message is given as

FORMULA FOR SUCCESS

Total number is given as n=17

Letter x Probability p(x)

F 2 2/17

O 2 2/17

R 2 2/17

M 1 1/17

U 2 2/17

L 1 1/17

A 1 1/17

S 3 3/17

C 2 2/17

E 1 1/17

Part b

The information is given as
`\sum{xp(x)}`

Letter x Probability p(x) xp(x)

F 2 2/17 4/17

O 2 2/17 4/17

R 2 2/17 4/17

M 1 1/17 1/17

U 2 2/17 4/17

L 1 1/17 1/17

A 1 1/17 1/17

S 3 3/17 9/17

C 2 2/17 4/17

E 1 1/17 1/17

______________________________________

Total 1.91

So the average information in this message is 1.91.