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)/ (Integral from ∞ to 0) R(x) f (x) dx
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
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
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)/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)/
Integral from R(x) f (x) dx
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)/
(Integral from ∞ to 0) R(x) f (x) dx
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