STAT 5100 Midterm: STAT 5100 Iowa Midterm1a
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Please write your answers in the exam books provided. You can use formulas from page 2 when appropriate: (5 points) a continuous random variable x has probability density function f (x) =(c(1 x4) 0 for 1 x 1 otherwise. (a) find the value of c. (b) find the cdf of x: (5 points) an urn contains three red and seven blue balls. A second urn contains six red and four blue balls. Two balls are selected at random from each urn without replacement. What is the probability that all four balls are the same color: (5 points) a box contains 10 items. The probability pk that k of the items are defective is k pk. Show, using this property and other basic properties of probability, that if b1 b2 b3 . is an in nite sequence of events, then is an in nite sequence of events such that t n=1 an = , then.
