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Chapter 6: Q. 22 (page 356)

22. Random numbers Let Ybe a number between0 and 1 produced by a random number generator. Assuming that the random variable Y has a uniform distribution, find the following probabilities:
(a) P(Y鈮�0.4)
(b) role="math" localid="1649593908596" P(Y<0.4)
(c) role="math" localid="1649593922659" P(0.1<Y鈮�0.15or0.77鈮�Y<0.88

Short Answer

Expert verified

(a) The probability for P(Y鈮�0.4)is 0.40

(b) The probability for P(Y<0.4 is 0.40

(c) The probability for role="math" localid="1649594539701" P(0.1<Y鈮�0.15or0.77鈮�Y<0.88)is 0.16.

Step by step solution

01

Part (a) Step 1: Given information 

To find the probability for P(Y鈮�0.4).

02

Part (a) Step 2: Explanation 

The variableY is following the uniform distribution.
The probability forP(Y鈮�0.4)can be determined as:
P(Y鈮�0.4)=(0.4-0)脳1=0.40

03

Part (b) Step 1: Given information

To find the probability for P(Y<0.4)

04

Part (c) Step 2: Explanation 

The variableY is following the uniform distribution.
The probability forP(Y<0.4) can be determined as:
P(Y<0.4)=(0.4-0)脳1=0.40

05

Part (c) Step 1: Given information 

To find the probability for P(0.1<Y鈮�0.15or0.77鈮�Y<0.88).

06

Part (c) Step 2: Explanation 

The probability forP(0.1<Y鈮�0.15or0.77鈮�Y<0.88) can be determined as:
P(0.1<Y鈮�0.15)=(0.15-0.1)脳1=0.05
P(0.77鈮�Y鈮�0.88)=(0.88-0.77)脳1=0.11

Then,

P(0.1<Y鈮�0.15or0.77鈮�Y鈮�0.88)=0.05+0.11=0.16

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Most popular questions from this chapter

Toss 4times Suppose you toss a fair coin 4times. Let X=the number of heads you get.

(a) Find the probability distribution ofX.

(b) Make a histogram of the probability distribution. Describe what you see.

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49. Checking independence In which of the following games of chance would you be willing to assume independence of Xandlocalid="1649903939419" Y in making a probability model? Explain your answer in each case.
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A large auto dealership keeps track of sales and leases agreements made during each hour of the day. Let X= the number of cars sold and Y= the number of cars leased during the 铿乺st hour of business on a randomly selected Friday. Based on previous records, the probability distributions of Xand Yare as follows:

顿别铿乶别 D=X-Y.

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