Problem 16E

Each of eight bearings in a bearing assembly has a diameter (in millimeters) that has the pdf

Assuming independence, find the cdf and the pdf of the maximum diameter (say, Y) of the eight bearings and compute P(0.9999 < Y < 1).

ST 701 Week Six Notes MaLyn Lawhorn September 19, 2017 and September 21, 2017 Transformation Continued Recall that if we have some random variable X with known PDF for which X ! Y by some g(x), then we also know everything we need to about Y .Depending on the properties of g(x), though, how we gather information about Y changes. Case 1: g(x) is one-to-one If g(x) is one-to-one, then this means that for each x 2 X, there is a unique value of x such that g(x) = y. An example would be if g(x) = 3x ▯ 4. An counter example would be g(x) = x 2 2 because for any y, there are two possible answers x = k and x = ▯k such that x = y. Case 1 is what wa