Answered: Let Y ∼ Wei(1, 23) (a) Compute E(Y) and…

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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Question

I. Let Y ∼ Wei(1, 23) (a) Compute E(Y) and Var(Y) (b) ComputeP(Y >1) II. Assume exam grades for STAT 370 are approximately normally distributed with a μ = 80 and σ = 6 (a) What exam grade would correspond to approximately the 90th percentile? (b) Approximately what percent of the exams fell below a grade of 85? (c) Approximately what percent of the exams fell between the grades of 55 and 75? (d) Graph the PDF (e) Graph the CDF III. A study was performed on wear of a bearing y and its relationship to x =oil viscosity. The following data were obtained. (problem similar to book) yx 50 21 53 10 2 11 2 45 (a) Compute and interpret the sample correlation coefficient. (do this calculation by hand) (b) Draw a scatterplot

Expert Solution

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Hello! As you have posted 3 different questions, we are answering the first question. In case you require the unanswered question also, kindly re-post them as separate question.

Given that Y ∼ Wei(1, 23).

That is, $α = 1 a n d β = 23$ .

$E (Y) = β Γ (1 + \frac{1}{α}) = 23 * Γ (1 + \frac{1}{1}) = 23 * Γ (2) = 23 * (2 - 1)! \sin c e, Γ (n) = (n - 1)! = 23$

$V a r (Y) = β^{2} [Γ (1 + \frac{2}{α}) - {[Γ (1 + \frac{1}{α})]}^{2}] = 23^{2} [Γ (1 + \frac{2}{1}) - {[Γ (1 + \frac{1}{1})]}^{2}] = 23^{2} [Γ (3) - {(Γ (2))}^{2}] = 23^{2} [(3 - 1)! - 1] = 23^{2} (2 - 1) = 529$