Question
{Exercise 6.27 (Algorithmic)} Consider the following exponential probability density function. f(x) = }e for > 0...
{Exercise 6.27 (Algorithmic)} Consider the following exponential probability density function. f(x) = }e for > 0 a. Which of the following is the formula for P(xs xo)? 1 P(x <=0) = 4- · 2 P(Z 520)=1-4- 3 P(1 520)=1-6-- Formula #2 b. Find P(x s 1) (to 4 decimals). C. Find P(x > 4) (to 4 decimals). 0.1353 d. Find P(x S 5) (to 4 decimals). e. Find P(1 3 x 5) (to 4 decimals).
Answers
Page 1 we have exponential probo density function f(x) = 1 12 1x70 © consider PCXXX.): -x/2 r = I te da [27:21 ] 1- e Xol2 PCXXI.): 1-22012) C consider, P(x20) = ft cxdx = Site de dx = = 0.39366 = 0.3935 P(X, 1) = 0.3935 ③ Now calculate, P( x I 4 ) PX > ***Jocandet 14 (2) dx stelleTI page 2 pcxv) : 1 2) { cada dia] = [o - e² - 0-1353 P(x>,4) = 0.1353] @ PCX55) = (fizode = seldz len - 5/2 = -[eel? = 0.9179 | P(x 55) = 0.9179] © P(1<x<5) = food items dx P(1 x ) 27 = 2 (-2) este - 0.5245 IP (ITX (5) = 0.5245)
![Page 1 we have exponential probo density function f(x) = 1 12 1x70 © consider PCXXX.): -x/2 r = I te da [27:21 ] 1- e Xol2 PC](http://img.homeworklib.com/questions/2f5b79f0-a217-11ea-8ffe-49dc619342e8.png?x-oss-process=image/resize,w_560)
![TI page 2 pcxv) : 1 2) { cada dia] = [o - e² - 0-1353 P(x>,4) = 0.1353] @ PCX55) = (fizode = seldz len - 5/2 = -[eel? = 0.917](http://img.homeworklib.com/questions/2ff12970-a217-11ea-ba3b-fb878c3397bf.png?x-oss-process=image/resize,w_560)
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