class_prob1 - number of maroon balls 3 Show that if n →...

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Class Problems on Bayes Rule and Discrete Random Variables 1. In a city 1% of the population has cancer. A cancer test is effective 98% of the time. If a person has been tested positive for cancer, what is the probability that he/she actually has cancer? 2. An urn contains 6 white and 4 maroon balls. if two balls are selected at random, obtain the pmf of the number of maroon balls in the selection. Also obtain the expected value of the
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Unformatted text preview: number of maroon balls. 3. Show that if n → ∞ and p → 0 such that np → λ , then Bin ( n,p ) → P ( λ ) in distribution. In other words, show that the PMF of a Bin ( n,p ) random variable equals that of a Poisson random variable with parameter λ as n → ∞ and p → 0 such that np → λ ....
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