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Chapter 3: Q13E (page 107)

An ice cream seller takes 20 gallons of ice cream in her truck each day. LetXstand for the number of gallons that she sells. The probability is 0.1 thatX=20. If she doesn鈥檛 sell all 20 gallons, the distribution ofXfollows a continuous distribution with a p.d.f. of the form


wherecis a constant that makes Pr(X <20)=0.9. Find the constantcso that Pr(X <20)=0.9 as described above.

Short Answer

Expert verified

The computed value of c is 0.0045.

Step by step solution

01

Given the information 

X is the random variable for the number of gallons sold by the seller of 20 gallons ice cream.

The probability that 20 gallons is sold is 0.1.

The random variable X follows a continuous distribution with a probability density function is,


The probability is given as P(X< 20)=0.9

02

Calculate the value of c

From the provided data, the value of c is computed as,

Therefore, the value of c is 0.0045.

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Suppose that a person鈥檚 score X on a mathematics aptitude test is a number between 0 and 1, and that his score Y on a music aptitude test is also a number between 0 and 1. Suppose further that in the population of all college students in the United States, the scores X and Y are distributed according to the following joint pdf:

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