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Let X refers the time to failure of a machine component. Suppose the pdf of X is f(x)=32/(x+4)^3 for x>0. The cdf is: F(x)=[6" 32 -dx (x+4)³ =6* 32 (x + 4)-3 dx (x+4)* )-3+1 =32

Let X refers the time to failure of a machine component. Suppose the pdf of X is f(x)=32/(x+4)^3 for x>0. The cdf is: F(x)=[6" 32 -dx (x+4)³ =6* 32 (x + 4)-3 dx (x+4)* )-3+1 =32

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Could you solve the part d, please?

Let X refers the time to failure of a machine component. Suppose the pdf of X is f(x)=32/(x+4)^3 for x>0. The cdf is: F(x)=[6° dx 32 3 (x+4)³ =6 32 (x + 4)-3 dx -3+1 jx (x+4) =32 -3+1 (x+4)-2 =32[ -2 1 =32 -2(x+4)² =32 -2)(x+4)* (-2)(0+4)? 1 =32 2(x+4)² 32 16 + 1 (x+4)? c. Use the previous result (part b) and calculate the probability that time to failure is between 6 and 4 unit of time. The CDF provide the probability of X <x. So to compute the probability between 4 and 6, the probability of X <4 can be subtracted from probability of X < 6. P(4<X<6)=P(X < 6) – P (X < 4) =F(6) – F(4) 16 16 + + (6+4)² 16 +1 100 + * - 1 =-0. 16 + 0. 25 =0. 09 d. What is the expected time until failure?
Transcribed Image Text:Let X refers the time to failure of a machine component. Suppose the pdf of X is f(x)=32/(x+4)^3 for x>0. The cdf is: F(x)=[6° dx 32 3 (x+4)³ =6 32 (x + 4)-3 dx -3+1 jx (x+4) =32 -3+1 (x+4)-2 =32[ -2 1 =32 -2(x+4)² =32 -2)(x+4)* (-2)(0+4)? 1 =32 2(x+4)² 32 16 + 1 (x+4)? c. Use the previous result (part b) and calculate the probability that time to failure is between 6 and 4 unit of time. The CDF provide the probability of X <x. So to compute the probability between 4 and 6, the probability of X <4 can be subtracted from probability of X < 6. P(4<X<6)=P(X < 6) – P (X < 4) =F(6) – F(4) 16 16 + + (6+4)² 16 +1 100 + * - 1 =-0. 16 + 0. 25 =0. 09 d. What is the expected time until failure?
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