Fundamentals of Applied Probability and Random Processes 2nd. Edition by Oliver C. Ibe | 9780128008522 | 0128008520

Statistical Mechanics

Fundamentals of Applied Probability and Random Processes

196 SOLVED PROBLEMS

Question: 12.11

Consider the state-transition diagram of Figure 12.12, which is a modified version of Figure 12.11. Here, the transition is now from state 2 to state 4 instead of from state 4 to state 2.For this case, states 1, 2,and 3 are now transient states because when the process enters state 2 and makes a ...

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Question: 4.23

If X∼N(3, 9), which means that X is a normal random variable with μX=3 and σX² =9, find the probability that X lies between 2 and 5. ...

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We are required to evaluate P[2 < X < 5], wh...

Question: 9.1

A random variable X is sampled 36 times obtaining a value X that is used as an estimate of E[X]. If the PDF of X is fX(x)=2e^-2x, where x≥0,a. Determine and E[X] and E[X²]. b. What is the probability that the sample mean lies between 1/4 and 3/4? ...

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a. Since

X

is an exponential random...

Question: 6.22

Assume that the random variable Sn is the sum of 48 independent experimental values of the random variable X whose PDF is given by fX (x)= {1/3 1≤x≤4 0 otherwise Find the probability that Sn lies in the range 108≤Sn≤126. ...

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The expected value and variance of

X[/latex...

Question: 6.4

(A more general case of Example 6.3) Obtain the PDF of Z=X+Y, where X and Y are two independent random variables with the following PDFs: fX (x)= {1/b-a a<x<b 0 otherwise fY (y)= 1/d-c c<y <d, d-c<b-a 0 otherwise ...

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The two PDFs are shown in Figure 6.6. To evaluate ...

Question: 6.3

Find the PDF of the sum of X and Y if the two random variables are independent random variables with the common PDF fX (u)=fY (u)= {1/4 0<u<4 0 otherwise ...

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The limits of integration of the PDF of

U=...

Question: 6.2

Find the PDF of the random variable Y=aX², where X is the standard normal random variable and a>0. ...

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The PDF of

X

is given by

\,\...

Question: 6.1

Find the PDF of Y in terms of the PDF of X if Y=2X+7. ...

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From the results obtained above,

\,\display...

Question: 5.16

The student population of a certain college in Massachusetts has been found to be made up as follows: 50% are from Massachusetts (or in-state students), 20% are from the other states of the United States (or out-of-state students), and 30% are from other countries (or foreign students). If 10 ...

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Let

K_1

be the number of in-state ...

Question: 5.15

A fair die is rolled 7 times. Find the probability that the number 1 appears twice and the number 2 appears once. ...

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The problem asks for the numbers 1 and 2. All the ...