Suppose that Y is a continuous random variable with distribution function given by F(y)
Chapter 4, Problem 4.191(choose chapter or problem)
Suppose that Y is a continuous random variable with distribution function given by F(y) and probability density function f (y). We often are interested in conditional probabilities of the form P(Y y|Y c) for a constant c. a Show that, for y c, P(Y y|Y c) = F(y) F(c) 1 F(c) . b Show that the function in part (a) has all the properties of a distribution function. c If the length of life Y for a battery has a Weibull distribution with m = 2 and = 3 (with measurements in years), find the probability that the battery will last less than four years, given that it is now two years old.
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