STAT 400 Lecture AL1 Examples for 3.2 (Part 1) Spring 2015 Dalpiaz Uniform Distribution over an interval [ a , b ] : For Uniform distribution, P ( c X d ) = d cb a, a c d b. E ( X ) = a b2, Var ( X ) = 12ab2)( . Exponential Distribution: otherwise00forθ1θxxf x e otherwise00forλλ xxf x e E ( X ) = , Var ( X ) = 2. E ( X ) = 1/, Var ( X ) = 1/2.1. Suppose the lifetime of a particular brand of light bulbs is exponentially distributed with mean of 400 hours. a) Find the probability that a randomly selected light bulb would last over 500 hours. b) Find the probability that 3 out of 7 randomly selected light bulbs would last over 500 hours. c) Find the probability that a randomly selected light bulb would last between 300 hours and 800
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