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Statistics / Mathematical Statistics with Applications 7 / Chapter 4 / Problem 4.12

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

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The length of time to failure (in hundreds of hours) for a transistor is a random

Chapter 4, Problem 4.12

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QUESTION:

The length of time to failure (in hundreds of hours) for a transistor is a random variable Y with distribution function given by F(y) = $ 0, y < 0, 1 ey2 , y 0.a Show that F(y) has the properties of a distribution function. b Find the .30-quantile, .30, of Y . c Find f (y). d Find the probability that the transistor operates for at least 200 hours. e Find P(Y > 100|Y 200).

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QUESTION:

The length of time to failure (in hundreds of hours) for a transistor is a random variable Y with distribution function given by F(y) = $ 0, y < 0, 1 ey2 , y 0.a Show that F(y) has the properties of a distribution function. b Find the .30-quantile, .30, of Y . c Find f (y). d Find the probability that the transistor operates for at least 200 hours. e Find P(Y > 100|Y 200).

ANSWER:

Step 1 of 6

(a).

Properties of a distribution function are given as:

and

If, thenfor any real numbersand.

The given function is:

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