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Chapter 15: Q12P (page 750)

Use Problemto 9find the expected value of the sum of the numbers on the dice in Problem2.

Short Answer

Expert verified

The expected value of the sum of the numbers on the dice is E(x+y)=7.

Step by step solution

01

Given Information

Two random variables defined over the same sample space.

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.

Two random variables defined over the same sample space.

x= number in first dice.

y= the number in second dice.

The average in first dice is given below.

μx=E(x)=∑xipi=16×(1+2+3+4+5+6)=3.5

Both dice are equal hence average of first dice is same as average of second type.

E(x+y)=E(x)+E(y)=3.5+3.5=7

Hence, the expected value of the sum of the numbers on the dice is E(x+y)=7

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