Pearson eText for Probability & Statistics for Engineers and Scientists with R -- Instant Access (Pearson+)
Pearson eText for Probability & Statistics for Engineers and Scientists with R -- Instant Access (Pearson+)
1st Edition
ISBN: 9780137548552
Author: Michael Akritas
Publisher: PEARSON+
Question
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Chapter 2.6, Problem 1E
To determine

Identify whether the events E1 and E2 are independent or not.

Expert Solution & Answer
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Answer to Problem 1E

The events E1 and E2 are not independent.

Explanation of Solution

Independent events:

Let A and B be two events are said to be independent if, if occurrence of event A does not influence occurrence of events B then events are referred as independent. The expression is, P(B|A)=P(B)

The event E1 denotes the first diode selected has efficiency below 0.28, and E2 denotes the second diode selected has efficiency above 0.35.

A sample of 10 laser diodes in which two have efficiency below 0.28, six have efficiency between 0.28 and 0.35, and two have efficiency above 0.35.

Two diodes are selected at random and without replacement.

The probability that the second diode selected has efficiency above 0.35 is,

P(E2)=210

The probability that the second diode selected has efficiency above 0.35 given that the first diode selected has efficiency below 0.28 is,

P(E2|E1)=29

It is clear that, P(E2|E1)P(E2) and events are not independent.

Hence, the events E1 and E2 are not independent.

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