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Chapter 15: Q14P (page 750)

As in Problem 11, show that the expected number of5's in n tosses of a die is n6.

Short Answer

Expert verified

Ex1,Ex2,Ex2,⋯,Exnall are equal.

The statement has been proven.

Step by step solution

01

Given Information

A coin is tossed twice.

02

Definition of the cumulative distribution function.

The likelihood that a comparable continuous random variable has a value less than or equal to the function's argument is the value of the function.

03

Prove the statement

A dice is tossed, the outcomes isS={1,2,3,4,5,6} .

E(x)=∑(1)xipin=(1)6

If the dice are tossed n times, then the expectation is given below.

Ex1+x2+⋯+xn=Ex1+Ex2+Ex2+⋯+Exn16+16+16+16+⋯=n6

Hence, Ex1,Ex2,Ex2,⋯,Exn all are equal.

Hence, the statement has been proven.

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