Question: Approximate P 39 75 X 41 25 where X is the
Approximate P(39.75 ≤ X ≤ 41.25), where X is the mean of a random sample of size 32 from a distribution with mean μ = 40 and variance σ2 = 8.
Answer to relevant QuestionsA random sample of size n = 18 is taken from the distribution with pdf f(x) = 1 − x/2, 0 ≤ x ≤ 2. (a) Find μ and σ2. (b) Find P(2/3 ≤ X ≤ 5/6), approximately. Let Y equal the sum of n = 100 Bernoulli trials. That is, Y is b(100, p). For each of (i) p = 0.1, (ii) p = 0.5, and (iii) p = 0.8, (a) Draw the approximating normal pdfs, all on the same graph. (b) Find P(| Y/100 − p | ...If the distribution of Y is b(n, 0.5), give a lower bound for P(|Y/n − 0.5| < 0.08) when (a) n = 100. (b) n = 500. (c) n = 1000. In Exercise 6.1-7, lead concentrations near the San Diego Freeway in 1976 are given. During the fall of 1977, the weekday afternoon lead concentrations (in μg/m3) at the measurement station near the San Diego Freeway in Los ...Let W1 < W2 < · · · < Wn be the order statistics of n independent observations from a U(0, 1) distribution. (a) Find the pdf of W1 and that of Wn. (b) Use the results of (a) to verify that E(W1) = 1/(n + 1) and E(Wn) = ...
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