Books are packed into cartons. The weight W of a book is a con-tinuous random variable with PDFfw (w) = λew w≥0The number K of books in any carton is a random variable with the PMFUkPK(k)=k = 0, 1, 2,...k!If we randomly select a carton and its weight is X, determinea. the s-transform of the PDF of X.b. E[X].c. the variance of X.

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Answered: Books are packed into cartons. The…

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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M3
Two Gaussian random variables X, and X, have zero mean and variances 0,²=4 and 0,² of new 2 %3D = 9. Their covariance Cx, equals 3. Find the covariance Cy. X2 random variables Y, and Y, if the transformation is given as 1 2 Y, = X, - 2X, Y, = 3X, +4X,
Probability and Stats
2. Semester test question: of the chi-square distribution is that if U and V are independent and U V~x, then U + V ~ X²+² x, and Show this using moment-generating functions. 3. Give the pdf of a random variable that is t distributed and has 2 degrees of freedom in the simplest form.
Suppose claim amounts at a health insurance company are independent of one another. In the first year calim amounts are modeled by a gamma random variable X with alpha=40, and beta=3. In the second year, individual claim amounts are modeled by random variable Y=1.05X+3. Let W be the average of 30 claim amounts in year two set up the equation to model the random variable W. a) Find the moment generating function of W b) Based on moment generating function of W is W also a gamma distribution? if so what are the parameters? c) Find the approximate probability that W is between 125$ and 130$.
solve it hand written part 3
Consider random variables X and Y with the joint PDF below find pxy
ele) Consider the regression model Y; = BX; + u; Where u, and X, satisfy the assumptions specified here. Let p denote an estimator of p that is constructed as ß= where Y and X are the sample means of Y, and X, respectively. Show that B is a linear function of Y,, Y2, Y Show that B is conditionally unbiased. 1 E(Y,X,, X2.. X,) = ▼ 1 „P(X, +X2+ + X,) + Y2 + + Yn) (AX, + u) 2 E(BIX,. X2 X,) =E |(X, X2.. Xn) Click to select your answer(s). W DELL P Type here to search 1/5
Let A and B be independent exponential random variables, both with mean 1. If U = A + B and V = A/B, find the joint pdf of U and V.
N1
1.STATISTICAL INFERENCE
Suppose that medical science has a cancer-diagnostic test that is 95% accurate on both those who do and those who do not have cancer. If 0.005 of the population actually has cancer, compute the probability that a particular individual has cancer, given that the test detected cancer.

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