## Question

###### 3) 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. 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 and 4 unit of time_d. What is the expected time until failure?

3) 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. 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 and 4 unit of time_ d. What is the expected time until failure?

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