21. An instrument is used to measure very small concentrations, X, of a certainchemical in soil samples. Suppose that the values of X in those soils in which thechemical is present is modeled as a random variable with density function f(x).The assay of a soil reports a concentration only if the chemical is first determinedto be present. At very low concentrations, however, the chemical may fail tobe detected even if it is present. This phenomenon is modeled by assuming thatif the concentration is x, the chemical is detected with probability R(x). Let Ydenote the concentration of a chemical in a soil in which it has been determinedto be present. Show that the density function of Y isg(y): =R(y) f (y)R(x) f(x) dx

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Answered: 1. An instrument is used to measure…

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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The random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0, otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y? (d) What is the correlation of X and Y?
Decide in each case whether the hypothesis issimple or composite:(a) the hypothesis that a random variable has a gammadistribution with α = 3 and β = 2;(b) the hypothesis that a random variable has a gammadistribution with α = 3 and β Z 2; (c) the hypothesis that a random variable has an expo-nential density; (d) the hypothesis that a random variable has a beta dis-tribution with the mean μ = 0.50.
This Wine Stinks. Are untrained students less sensitive on the average than trained tasters in detecting "off odors" in wine?Example 3 (The question before this) gives the lowest levels of dimethyl sulfide (DMS) that 10 students could detect. (31, 31, 43, 36, 23, 34, 32, 30, 20, 24). Assume that the odor threshold for untrained noses is Normal distributed with σ = 7 ug/l. Is there evidence that the mean threshold for untrained tastes is greater than 25 μg/l?
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Do fast i will give like soon
Suppose the random variable, X, follows a geometric distribution with parameter 0 (0 < 0 < 1). Let X₁, X2,..., X be a random sample of size n from the population of X. (a) Write down the likelihood function of the parameter. (b) Show that the log likelihood function of depends on the sample only through Σj=1 Xj. (c) Find the maximum likelihood estimator (mle) of 0. (d) Find the method of moments estimator (mme) of 0.

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