1. Let X₁, X₂, and X3 represent the times necessary to perform three successive repairs tasks at acertain service facility. Suppose they are independent, normal random variables with expectedvalues µ µ², and µ and variances σ²,02, and o3, respectivelya) If μ₁ = μ₂ = μ₂ = 60 and σ² = σ² = 3 =15, calculate P(X₁ + X₂ + X3 ≤ 200).b) Using the u's and o's given in part (a), calculate P(58 ≤ X ≤ 62), whereX = X₁ + X₂+X313c) Using the u's and o's given in part (a), calculate P(-10 ≤X₁ −0.5X₂ – 0.5X3 ≤5).d) If µ = 40, µ = 50, µ = 60, o² =10, o² =12, and o² =14, calculate P(X₁ + X₂ − 2X3 ≥ 0).

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Answered: 1. Let X₁, X₂, and X3 represent the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A certain mutual fund invests in both U.S. and foreign markets. Let x a random variable that represents the monthly percentage return for the fund. Assume x has mean u = 1.9% and standard deviation o = 0.3%. (a) The fund has over 175 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for the fund is itself an average return computed using all 175 stocks in the fund. Why would this indicate that x has an approximately normal distribution? Explain. Hint: See the discussion after Theorem 6.2. The random variable -Select-v is a mean of a sample size n = 175. By the -Select- v, the -Select- distribution is approximately normal. (b) After 6 months, what is the probability that thẹ average monthly percentage return x will be between 1% and 2%? Hint: See Theorem 6.1, and assume that x has…
Consider a hypothesis test of difference of means for two independent populations x1 and x2.
Let X,, X,, and x, represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values 4,, Hz, and uz and variances o,2, 0,2, and o,2, respectively. (Round your answers to four decimal places.) A USE SALT 2 (a) If H1 = H2 = H3 = 60 and o,? = 0,2 . = 18, calculate P(T, s 204) and P(144 s T, s 204). P(T, s 204) = 0.9995 P(144 s T,s 204) = (b) Using the us and os given in part (a), calculate both P(54 s X) and P(58 s Xs 62). P(54 s X) P(58 s Xs 62) = 0.568 0.568 %3D (c) Using the u's and o's given in part (a), calculate P(-12 s X, - 0.5X2 - 0.5X3 s 6). P(-12 s X, - 0.5X, - 0.5x, s 6) = 0.8665
Assume X and Y are independent random variables with X ~ Binomial(n =100, p = 0.2) and Y ~ Pascal(m =16, p = 2/3) . Find the indicated expected value and variance. a. E(3X + 2Y +1) b. Var(3X + 2Y +1)
Let Y₁, Y₂, ..., Y₁ denote a random sample from a normal distribution with unknown mean and unknown variance o². For testing Ho: o² = 0 vs. Ha: o²o, show that the a-level Likelihood Ratio Test (LRT) is equivalent to the x² test
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