Let Ybe an exponentially distributed random variable with mean 3. Define a random variable X in thefollowing way: X= kif k-1 ≤Y

Y is an exponential random variable with mean β . Therefore, the PDF of Y is:Result:∫eaxdx=eaxa

Answered: Let Ybe an exponentially distributed…

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) Let Y be a random variable distributed as X. Determine E(Y) in terms of r. (b) Let {X1, X2, . .. , Xn} be a random sample drawn from a normal distirbution with mean u and 1 variance o?. Denote S E-(X; – X)² as the sample standard deviation. Use the 1 n - result in part (a), or otherwise, to find E(S). (c) Find an unbiased estimator for the population standard deviation o.
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Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…
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Let Ybe an exponentially distributed random variable with mean ß. Define a random variable X in the following way: X= kif k- 1 ≤ Y