function f(z) = Ae-;0< I<∞(A > 0). Define a new random variable Y = xi. (a) Show that the cumulative density function of Y is given by Fy (y) = (-exp(-Ay": and hence, or otherwise, find the probability density function of Y. (b) Find an expression for the maximum likelihood estimator of the parameter A, using a sample Y1. 92, , Yn, from the distribution of Y.
function f(z) = Ae-;0< I<∞(A > 0). Define a new random variable Y = xi. (a) Show that the cumulative density function of Y is given by Fy (y) = (-exp(-Ay": and hence, or otherwise, find the probability density function of Y. (b) Find an expression for the maximum likelihood estimator of the parameter A, using a sample Y1. 92, , Yn, from the distribution of Y.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...
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Transcribed Image Text:5. Suppose that the random variable X follows an exponential distribution with probability density
function
S(z) = de-A";0 < x < ∞(A > 0).
Define a new random variable Y = x.
(a) Show that the cumulative density function of Y is given by Fy(y) = {-exp(-Ay";
and hence, or otherwise, find the probability density function of Y.
(b) Find an expression for the maximum likelihood estimator of the parameter A, using a sample
Y1, 92, , Yn, from the distribution of Y.
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