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. a. Verify that if the f(x) is a legitimate pdf. b. Determine the cdf. c. Use the previous result (part b) and calculate the probability that time to failure is between I and 4 unit of time. d. What is the expected time until failure?
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. a. Verify that if the f(x) is a legitimate pdf. b. Determine the cdf. c. Use the previous result (part b) and calculate the probability that time to failure is between I and 4 unit of time. d. What is the expected time until failure?
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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please solve the only part d
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.
a. Verify that if the f(x) is a legitimate pdf.
b. Determine the cdf.
c. Use the previous result (part b) and calculate the probability that time to failure is between I and 4
unit of time.
d. What is the expected time until failure?
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Step 1
d) E[X] =4
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