(a) Let X be a continuous random variable representing the time to failure of a computer...

 

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(a) Let X be a continuous random variable representing the time to failure of a computer with the probability density function: f(x) -{3 0 Ikea 20 *<0 i) Find the value of k. ii) Calculate the probability that the computer fails between 50 and 150 hours. iii) Calculate the probability that the computer fails before 100 hours. iv) Calculate the probability that the computer fails before 150 hours, condi- tional on the computer working for more than 100 hours. (b) Let X be a random variable. X has the following probability distribution: -1 01 P(X) 1/5 2/5 2/5 What is the probability distribution of W = X² (e) The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x) 19x210 0 ≤ 10 i) Determine the cumulative distribution function of X. ii) Determine the mode (point of maximum density), and the median (m such that P(X ≤m) = F(m) = 0.5). iii) What is the probability that of 6 such devices at least 5 of them will function for at least 20 hours? (a) Let X be a continuous random variable representing the time to failure of a computer with the probability density function: f(x) -{3 0 Ikea 20 *<0 i) Find the value of k. ii) Calculate the probability that the computer fails between 50 and 150 hours. iii) Calculate the probability that the computer fails before 100 hours. iv) Calculate the probability that the computer fails before 150 hours, condi- tional on the computer working for more than 100 hours. (b) Let X be a random variable. X has the following probability distribution: -1 01 P(X) 1/5 2/5 2/5 What is the probability distribution of W = X² (e) The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f(x) 19x210 0 ≤ 10 i) Determine the cumulative distribution function of X. ii) Determine the mode (point of maximum density), and the median (m such that P(X ≤m) = F(m) = 0.5). iii) What is the probability that of 6 such devices at least 5 of them will function for at least 20 hours?