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Chapter 5: Q.5.33 (page 214)

The number of years a radio function is exponentially distributed with the parameterλ=18If Jones buys a used radio, what is the probability that it will be working after an additional8year?

Short Answer

Expert verified

The probability that it will be working

after an additional8year is e-1

Step by step solution

01

Given Information.

The number of years a radio function is exponentially distributed with parametersλ=18.

02

Explanation.

Let Xbe the number of years a radio functions. We do not know the age of Jones's second-hand ratio-but given that it is still functioning, we can assume its age is the expected value Xgiven byE(X)=1λ=118=8

03

Explanation.

Hence, the conditional probability that Jones's ratio functions for another year would be given by

P(X≥16|X≥8)=P(X≥16;X≥8)P(X≥8)

04

Explanation.

Of Course,P(X≥16;X≥8)=P(X≥16)

05

Explanation.

Thus P(X≥16|X≥8)=P(X≥16)P(X≥8)

=e-18.16e-18.8=e-1

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Most popular questions from this chapter

Two types of coins are produced at a factory: a fair coin and a biased one that comes up heads 55percent of the time. We have one of these coins but do not know whether it is a fair coin or a biased one. In order to ascertain which type of coin we have, we shall perform the following statistical test: We shall toss the coin 1000 times. If the coin lands on heads 525 or more times, then we shall conclude that it is a biased coin, whereas if it lands on heads fewer than 525 times, then we shall conclude that it is a fair coin.

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