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Chapter 5: Q5E (page 325)

Sketch the p.d.f. of the exponential distribution for each of the following values of the parameter 尾:(a)\(\beta = \frac{1}{2}\),(b)\(\beta = 1\), and (c)\(\beta = 2\)

Short Answer

Expert verified

a. The p.d.f for\(\beta = \frac{1}{2}\)is as shown in Fig (a).

b. The p.d.f for\(\beta = 1\)is as shown in Fig (b).

c. The p.d.f for \(\beta = 2\)is as shown in Fig (c).

Step by step solution

01

Sketching the p.d.f. of exponential distribution for \(\beta  = \frac{1}{2}\)

Steps to draw the graph for exponential distribution are as follows:

1. Take\(\beta = \frac{1}{2}\)in p.d.f of exponential distribution.

2. Take different values of random variable X on x-axis and corresponding value of\(f\left( x \right)\)on y- axis and the p.d.f on y axis.

3. Draw the graph for the particular values of \(\beta \)

02

 Step 2: Sketching the p.d.f. of exponential distribution for \(\beta  = 1\)

Steps to draw the graph for exponential distribution are as follows:

1. Take\(\beta = 1\)in p.d.f of exponential distribution.

2. Take different values of random variable X on x-axis and corresponding value of\(f\left( x \right)\)on y- axis and the p.d.f on y axis

3. Draw the graph for the particular values of \(\beta \)

03

Sketching the p.d.f. of exponential distribution for \(\beta  = 2\)

Steps to draw the graph for exponential distribution are as follows:

1. Take\(\beta = 2\)in p.d.f of exponential distribution.

2. Take different values of random variable X on x-axis and corresponding value of\(f\left( x \right)\)on y- axis and the p.d.f on y axis.

3. Draw the graph for the particular values of \(\beta \)

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