50. Let X₁, X2, ..., X50 be i.i.d. with E(X) = 25 and V(X₂) = 10. Consider the random variable defined by50 X₁the sample average X = Σ Apply the Central Limit Theorem to answer the following:ni=1(a) What is the approximate distribution of X (include parameter(s))?(b) Approximate P(X> 25.5).(c) Approximate P(|X-25 <0.8).(d) Approximate the 0.975 quantile (97.5th%tile) of X.

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Answered: 50. Let X₁, X2,..., X50 be i.i.d. with…

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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The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630
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a) Let X₁, X2, X3,..., X₁ be a random sample of size n from population X. Suppose that X follows an exponential distribution with parameter 0 and Y = ===1 X₁. n b) i) Show that y follows a chi-square distribution with 2n degrees of freedom. ii) What is the value of the sample size n, if P(Y > 20.4831) = 0.025? iii) What is the value of sample size n, if P(|Y - 2n| <40) ≥ 0.025? iv) Use the Central Limit Theorem to compute P(100 < Y < 115), for n = 40. Let X₁, X2, ..., X5 be a random sample of size 5 from the standard normally population. If the statistic Y is given by Y = X1 X2 X3 ₁²+X3² +X5² i) Briefly explain why Y follows a Student's t distribution with 3 degrees of freedom. ii) Compute the probability that Y is between 2.35 and 5.84. iii) What is the mean and variance of the statistic Y?
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