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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.

渭x=E(x)=鈭�xipi=16脳(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) There are 10 chairs in a row and 8 people to be seated. In how many ways can this be done?

(b) There are 10 questions on a test and you are to do 8 of them. In how many

Ways can you choose them?

(c) In part (a) what is the probability that the first two chairs in the row are vacant?

(d) In part (b), what is the probability that you omit the first two problems in the

test?

(e) Explain why the answer to parts (a) and (b) are different, but the answers to

(c) and (d) are the same.

Computer plot on the same axes the normal density functions with 渭=0蟽=1and, 2, and 5. Label each curve with its蟽.

There are 3 red and 2 white balls in one box and 4 red and 5 white in the second box. You select a box at random and from it pick a ball at random. If the ball is red, what is the probability that it came from the second box?

(a) One box contains one die and another box contains two dice. You select a box at random and take out and toss whatever is in it (that is, toss both dice if you have picked box 2 ). Let x=number of 3'sshowing. Set up the sample space and associated probabilities for x .

(b) What is the probability of at least one3?

(c) If at least one 3 turns up, what is the probability that you picked the first box?

(d) Find xand.蟽

Question: Use both the sample space (2.4) and the sample space (2.5) to answer the following questions about a toss of two dice.

(a) What is the probability that the sum is 鈮� 4?

(b) What is the probability that the sum is even?

(c) What is the probability that the sum is divisible by 3?

(d) If the sum is odd, what is the probability that it is equal to 7?

(e) What is the probability that the product of the numbers on the two dice is 12?
See all solutions

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