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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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Most popular questions from this chapter

A so-called 7-way lamp has three 60-watt bulbs which may be turned on one or two or all three at a time, and a large bulb which may be turned to 100 watts, 200 watts or300 watts. How many different light intensities can the lamp be set to give if the completely off position is not included? (The answer is not 7.)

A card is drawn from a shuffled deck. Let x=10if it is an ace or a face card; x=−1if it is a2 ; andx=0 otherwise.

A card is selected from a shuffled deck. What is the probability that it is either a king or a club? That it is both a king and a club?

Two dice are thrown; x = sum of the numbers on the dice

Use Bayes’ formula (3.8) to repeat these simple problems previously done by usinga reduced sample space.

(a) In a family of two children, what is the probability that both are girls if at

least one is a girl?

(b) What is the probability of all heads in three tosses of a coin if you know that

at least one is a head?
See all solutions

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