Trainees must complete a specific task in less than 2 minutes. Consider the probability density function below for the time it t
akes a trainee to complete the task.f(x) = 0.85 - 0.35x0 < x < 2a) What is the probability a trainee will complete the task in less than 1.31 minutes? Give your answer to four decimal places.b) What is the probability that a trainee will complete the task in more than 1.31 minutes? Give your answer to four decimal places.c) What is the probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task? Give your answer to four decimal places.d) What is the expected time it will take a trainee to complete the task? Give your answer to four decimal places.e) If X represents the time it takes to complete the task, what is E(X2)? Give your answer to four decimal places.f) If X represents the time it takes to complete the task, what is Var(X)? Give your answer to four decimal places.
If f(x) = 0.85-0.35x (0<x<2) is the <em>PDF</em> and X is the random variable that measures the time it takes for a trainee to complete the task, the probability a trainee will complete the task in less than 1.31 minutes is P(X<1.31)
b)
The probability that a trainee will complete the task in more than 1.31 minutes is
P(X>1.31) = 1 - P(X<1.31) = 1 - 0.8132 = 0.1868
c)
The probability it will take a trainee between 0.25 minutes and 1.31 minutes to complete the task is P(0.25<X<1.31)
d)
the expected time it will take a trainee to complete the task