# Extra - Extra problems for additional credit 1 Derive the...

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Extra problems for additional credit. 1. Derive the formula for the mean and standard deviation of a discrete uniform random variable over the range of integers a, a + 1 , . . . , b . 2. A bearing assembly contains 10 bearings. The bearing diameters are assumed to be independent and normally distributed with a mean of 1.5 mm and a standard deviation of 0.025 mm. What is the probability that the
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Unformatted text preview: maximum diameter bearing assembly exceeds 1.6 mm? 3. Suppose that X 1 ,X 2 ,...,X n is a random sample from a continuous probability distribution with median ˜ μ . a) Show that P { min( X i ) < ˜ μ < max( X i ) } = 1-‡ 1 2 · n-1 . b) Write down an 100(1-α ) conﬁdence interval for the median ˜ μ where α = ‡ 1 2 · n-1 . 1...
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