Let X1,..., X8 be a sample from a normal population with population mean μ =16 and population variance σ ^2 =1.5. Let X and S^2 denote the sample mean and sample variance. (a) Find P{15.5 < X < 16.2}. (b) Express P{S^2 ≥ 1.7} in terms of a chi-square random variable. (c) Find the conditional probability P({15.5 < X < 16.2}|{S^2 ≥ 1.7}).

Let X1,..., X8 be a sample from a normal population with population mean μ =16 and population variance σ ^2 =1.5. Let X and S^2 denote the sample mean and sample variance. (a) Find P{15.5 < X < 16.2}. (b) Express P{S^2 ≥ 1.7} in terms of a chi-square random variable. (c) Find the conditional probability P({15.5 < X < 16.2}|{S^2 ≥ 1.7}).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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