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Chapter 4: Q.4.6 (page 163)

In Problem 4.5,for n=3,if the coin is assumed fair, what are the probabilities associated with the values that X can take on?

Short Answer

Expert verified

For n=3,

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

Step by step solution

01

Step1: Given Information

X - It is the difference between the number of heads and the number of tails.

02

Step2: Explanation

Possible outcomes of X, when a coin is tossed n times are:

If the number of tails is t, then the number of heads(h) is n-t.

h=n-t

Therefore X can be written as:

X=h-t=n-t-t=n-2t

Therefore possible outcomes of X are:

{n-2t∣t∈{0,1,…,n}}

Here localid="1646472975417" n=3,

The result is {3-2t∣t∈{0,1,2,3}}

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

03

Step3: Final Result

X=3-2tX=3H,H,HP=18X=1H,T,HT,H,HH,H,TP=38X=-1T,T,HT,H,TH,T,TP=38X=-3T,T,TP=18

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