# Question: Let X be a random variable with support 1 2

Let X be a random variable with support {1, 2, 3, 5, 15, 25, 50}, each point of which has the same probability 1/7. Argue that c = 5 is the value that minimizes h(c) = E( |X − c| ). Compare c with the value of b that minimizes g(b) = E[(X − b)2]

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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 Let μ and σ2 denote the mean and variance of the random variable X. Determine E[(X − μ)/σ] and E{[(X − μ)/σ]2}. In group testing for a certain disease, a blood sample was taken from each of n individuals and part of each sample was placed in a common pool. The latter was then tested. If the result was negative, there was no more ...Use the result of Exercise 2.5-5 to find the mean and variance of the (a) Bernoulli distribution. (b) Binomial distribution. (c) Geometric distribution. (d) Negative binomial distribution. Let f(x) = 1/2, −1 ≤ x ≤ 1, be the pdf of X. Graph the pdf and cdf, and record the mean and variance of X.Post your question