Calculate the mean for the random variable in Exercise

Chapter 3, Problem 75E

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QUESTION:

Calculate the mean for the random variable in Exercise 3-37.

3-37. Consider the circuit in Example 2-32. Assume that devices fail independently. What is the probability mass function of the number of failed devices?

Example 2-32

Series Circuit The following circuit operates only if there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that devices fail independently. What is the probability that the circuit operates?

Let L and R denote the events that the left and right devices operate, respectively. There is a path only if both operate. The probability that the circuit operates is

P(L and R) = \(P(L \cap R)=P(L) P(R)=0.80(0.90)=0.72\)

Practical Interpretation: Notice that the probability that the circuit operates degrades to approximately 0.5 when all devices are required to be functional. The probability that each device is functional needs to be large for a circuit to operate when many devices are connected in series.

Equation transcription:

Text transcription:

P(L \cap R)=P(L) P(R)=0.80(0.90)=0.72

Questions & Answers

QUESTION:

Calculate the mean for the random variable in Exercise 3-37.

3-37. Consider the circuit in Example 2-32. Assume that devices fail independently. What is the probability mass function of the number of failed devices?

Example 2-32

Series Circuit The following circuit operates only if there is a path of functional devices from left to right. The probability that each device functions is shown on the graph. Assume that devices fail independently. What is the probability that the circuit operates?

Let L and R denote the events that the left and right devices operate, respectively. There is a path only if both operate. The probability that the circuit operates is

P(L and R) = \(P(L \cap R)=P(L) P(R)=0.80(0.90)=0.72\)

Practical Interpretation: Notice that the probability that the circuit operates degrades to approximately 0.5 when all devices are required to be functional. The probability that each device is functional needs to be large for a circuit to operate when many devices are connected in series.

Equation transcription:

Text transcription:

P(L \cap R)=P(L) P(R)=0.80(0.90)=0.72

ANSWER:

Solution:

Step 1 of 2:

A circuit consist of two devices which connected parallely.

The device failed independently.

The probability that each device functions is 0.8 and 0.9 respectively.

So the probability that each device failed is 0.2 and 0.1 respectively.

We have to find the mean of the random variable X.


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