1. Two efficiency experts take independent measurements Y₁ and Y₂ on the length of time workers take to complete a certain task. Each measurement is assumed to have the probability density function given by fy(y) = favoz. 0, y > 0 otherwise (a) Find the moment generating function of Y₁. Clearly show your steps. Y₁+Y₂ 2 Clearly show your steps. (b) Find the probability density function for the average X = (c) Find E(X) and V(X). Justify your answers. (d) Suppose that X₁, X2, ....X100 are 100 independent observations from a probability distribution of X and X is the sample mean of the random sample. How can the value xo such that P(X < xo) = 0.90 be found in R? Select the appropriate R function from those listed below, and write down the R code, with the arguments filled in appropriately, that would give the value xo such that P(X < xo) = = 0.90. Note that you do not need to report a numerical answer here. Some R functions are included here for your reference: pexp (a, rate), qexp (a, rate), dexp (a, rate), pnorm (a, mean, sd), qnorm (a, mean, sd), dnorm (a, mean, sd), punif (a, min, max), qunif (a, min, max), dunif (a, min, max), qgamma (a, alpha, rate), dgamma (a, alpha, rate) pgamma (a, alpha, rate),

1. Two efficiency experts take independent measurements Y₁ and Y₂ on the length of time workers take to complete a certain task. Each measurement is assumed to have the probability density function given by fy(y) = favoz. 0, y > 0 otherwise (a) Find the moment generating function of Y₁. Clearly show your steps. Y₁+Y₂ 2 Clearly show your steps. (b) Find the probability density function for the average X = (c) Find E(X) and V(X). Justify your answers. (d) Suppose that X₁, X2, ....X100 are 100 independent observations from a probability distribution of X and X is the sample mean of the random sample. How can the value xo such that P(X < xo) = 0.90 be found in R? Select the appropriate R function from those listed below, and write down the R code, with the arguments filled in appropriately, that would give the value xo such that P(X < xo) = = 0.90. Note that you do not need to report a numerical answer here. Some R functions are included here for your reference: pexp (a, rate), qexp (a, rate), dexp (a, rate), pnorm (a, mean, sd), qnorm (a, mean, sd), dnorm (a, mean, sd), punif (a, min, max), qunif (a, min, max), dunif (a, min, max), qgamma (a, alpha, rate), dgamma (a, alpha, rate) pgamma (a, alpha, rate),

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.CR: Chapter 13 Review

Problem 29CR

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