Unformatted text preview: 3. A player throws darts at a target. On each trial, independently of the other trials, he hits the bull'seye with probability .05. How many times should he throw so that his probability of hitting the bull'seye at least once is .5? 4. The following table shows a cumulative distribution function (cdf) of a discrete random variable: (a) Find the probability mass function (pmf). (b) Find f(3.3) and F(3.3) 5. Let ? ( ± ) = 1 − exp( −²± ³ ) , ´µ ± ≥ , ´µ ± < 0 , for some constants ² , ³ > 0 . (a) Show that ? ( ± ) is a proper cdf. (b) Find the probability density function (pdf). (c) Find ± such that ¶ ( · > ± ) = 0.1 . 6. Suppose that · has the density function µ ( ± ) = ¸±¹ −º± , ± ≥ , ± < 0 where º > 0 is a constant. (a) Find the value of ¸ . (b) Find the cdf. (c) Find ¶ (0 < · < 1 º ) . k 0 1 2 3 4 5 F(k) 0 .1 .3 .7 .8 1...
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 Fall '10
 MrChung
 Statistics, Probability, Diabetes, Probability distribution, Probability theory, Cumulative distribution function, Probability mass function

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