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Chapter 4: Q.4.26 (page 165)

One of the numbers 1through 10is randomly chosen. You are to try to guess the number chosen by asking questions with 鈥測es-no鈥� answers. Compute the expected number of questions you will need to ask in each of the following two cases:

(a) Your ith question is to be 鈥淚s it i?鈥� i = 1,2,3,4,5,6,7,8,9,10. (b) With each question, you try to eliminate one-half of the remaining numbers, as nearly as possible.

Short Answer

Expert verified
  1. Your ith question is to be112
  2. The number of question is3.463.46

Step by step solution

01

Given Information (Part a)

Given in the question that, randomly chosen numbers 1 through 10.

We need to compute the expected number of questions to ask ith question is to be " is it i?".

02

Explanation (Part a)

E[X]=1脳110+2脳110+3脳110+4脳110+5脳110+6脳110+7脳110+8脳110+9脳110+10脳110

Because Pof every digit =110

E[X]=110[1+2+3+4+5+6+7+8+9+10]

=110脳10脳112

=112

03

Final Answer (Part a)

The expected number of question is112.

04

Given Information (Part b)

Given in the question that, randomly chosen numbers 1 through 10.

We need to compute the expected number of questions with each question, you try to eliminate one half of the remaining numbers, as nearly as possible

05

Explanation (Part a)

We need to apply Binary search here,

2n=11

nis number of questions

nln2=ln11

n=ln11ln2

=3.46

06

Final Answer (Part a)

The number of questions is 3.46

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