1. An instrument is used to measure very small concentrations, X, of a certain chemical in soil samples. Suppose that the values of X in those soils in which the chemical 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 determined to be present. At very low concentrations, however, the chemical may fail to be detected even if it is present. This phenomenon is modeled by assuming that if the concentration is x, the chemical is detected with probability R(x). Let Y denote the concentration of a chemical in a soil in which it has been determined to be present. Show that the density function of Y is g(y)= R(y) f (y) R(x) f(x) dx
1. An instrument is used to measure very small concentrations, X, of a certain chemical in soil samples. Suppose that the values of X in those soils in which the chemical 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 determined to be present. At very low concentrations, however, the chemical may fail to be detected even if it is present. This phenomenon is modeled by assuming that if the concentration is x, the chemical is detected with probability R(x). Let Y denote the concentration of a chemical in a soil in which it has been determined to be present. Show that the density function of Y is g(y)= R(y) f (y) R(x) f(x) dx
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...
Related questions
Question
Transcribed Image Text:21. An instrument is used to measure very small concentrations, X, of a certain
chemical in soil samples. Suppose that the values of X in those soils in which the
chemical 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 determined
to be present. At very low concentrations, however, the chemical may fail to
be detected even if it is present. This phenomenon is modeled by assuming that
if the concentration is x, the chemical is detected with probability R(x). Let Y
denote the concentration of a chemical in a soil in which it has been determined
to be present. Show that the density function of Y is
g(y): =
R(y) f (y)
R(x) f(x) dx
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
