Jones figures that the total number of thousands of miles that an auto can be driven before it would need to be junked is an exponential random variable with parameter 1/20. Smith has a used car that he claims has been driven only 10,000 miles. If Jones purchases the car, what is the probability that she would get at least 20,000 additional miles out of it? Repeat under the assumption that the lifetime mileage of the car is not exponentially distributed, but rather is (in thousands of miles) uniformly distributed over (0, 40).
Answer to relevant QuestionsSuppose that the life distribution of an item has the hazard rate function λ(t) = t3, t > 0. What is the probability that (a) The item survives to age 2? (b) The item’s lifetime is between .4 and 1.4? (c) A 1-year-old ...Compute E[X] if X has a density function given by (a) (b) (c) The median of a continuous random variable having distribution function F is that value m such that F(m) = 1/2. That is, a random variable is just as likely to be larger than its median as it is to be smaller. Find the ...If X is a beta random variable with parameters a and b, show that E[X] = a/a + b Var(X) = ab/(a + b)2(a + b + 1) The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is (a) Show that 1/c = area of region R. Suppose that (X, Y) is uniformly distributed over ...
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