To find the variance of a hyper-geometric random variable in Example 2.3-4 we used the fact that
Prove this result by making the change of variables k = x − 2 and noting that
Answer to relevant QuestionsLet X equal the number of people selected at random that you must ask in order to find someone with the same birthday as yours. Assume that each day of the year is equally likely, and ignore February 29. (a) What is the pmf ...Place eight chips in a bowl: Three have the number 1 on them, two have the number 2, and three have the number 3. Say each chip has a probability of 1/8 of being drawn at random. Let the random variable X equal the number on ...Suppose that in Exercise 2.4-1, X = 1 if a red ball is drawn and X = −1 if a white ball is drawn. Give the pmf, mean, and variance of X. The mean of a Poisson random variable X is μ = 9. Compute P(μ − 2σ < X < μ+ 2σ). Nicol lets the pdf of X be defined by Find (a) The value of c so that f(x) is a pdf. (b) The mean of X (if it exists). (c) The variance of X (if it exists). (d) P(1/2 ≤ X ≤ 2).
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