A particular pumping engine will only function properly if an essential component functions properly. The time to failure of the component ( in thousands of hours) is a random variable X with probability density f(x) = 0.02xe-0.01x^2 for x > 0. What is the proportion of pumping engines that will not fail before 10,000 hours of use? What is the probability that the engine will survive for another 5000 hours, given that it has functioned properly during the past 5000 hours?

22. The life X in months of a certain light bulb is a random variable with exponential density. What is the probability that the light bulb will have a life span between 25 and 30 months if its average life is 20 months?

Plot the probability mass and distribution functions of the binomial random variable X with parameters (n=2, p=1/2).

Suppose that the time (in hours) required to repair a machine is an exponentially distributed random variable with parameter λ=0.9. What is(a) the probability that a repair time exceeds 9 hours? (b) the conditional probability that a repair takes at least 10 hours, given that it takes more than 7 hours?

Let random variable X denote the length of a wire, assumed to be exponentially distributed with mean 107 cm. The wire is cut to make rings of radius 1 cm. Derive the probability mass function for the number of complete rings that can be produced by each length of wire.

The time it takes to travel from my apartment to work is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability that my commute time tomorrow will take between 30 and 35 minutes?(please round your answer to 2 decimal places)

Suppose the weight of pieces of passenger luggage for domestic airline flights follows a normal distribution with u = 28 pounds and o = 5.5 pounds. (a) Calculate the probability that a piece of luggage weighs less than 32 pounds. (Assume that the minimum weight for a piece of luggage is 0 pounds.) (b) Calculate the weight where the probability density function for the weight of passenger luggage is increasing most rapidly. Ib (c) Use the Empirical Rule to estimate the percentage of bags that weigh more than 17 pounds. (d) Use the Empirical Rule to estimate the percentage of bags that weigh between 22.5 and 39. (e) According to the Empirical Rule, about 84% of bags weigh less than pounds. Submit Answer View Previous Question Question 4 of 7 View Next Question Home My Assignments Request Extension 11:16 AM W) 59°F P Type here to search 10/19/2021 4 BA ins prt sc delete home end f10 12 f3 米 f4 f5 f6 10 fg & num + backspace lock 2 3. 4 6. 7. 00 II %24 %23

The time taken by brake discs to overheat on construction equipment is normally distributed with µ=4.5 and ơ=0.45 What is the probability that the time to overheat is less than 3.8 minutes?

Consider a random variable V modeling the version of the software that people have installed on their computers, where the possible versions are {1, 2, 3, 4}. People are equally likely to have versions 1 and 2 and also equally likely to have versions 3 and 4. People are also x times more likely to have version 3 than version 2. (a) What is the (probability mass function) PMF of V as a function of x (b) What is the expected version of the software. Hint: the expected value of V as a function of x (c) What is the minimum value of x to ensure that the mean version is at least version 3?

Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?