•(v) (a) Find E (Y), E (Y²) and Var(Y). (b) A random sample Y1, Y2, . , Yn is taken from Y - Exp(1). Write down the likelihood function I(1) and find the maximum likelihood estimator (MLE) of 1. (c) The lifetime T (years) of an electronic component follows ali exponential distribution Exp(1) (i) Find the lifetime L which a typical component is 60% certain to exceed. (ii) If five components are sold to a manufacturer, find the probability that at least one of them will have a lifetime less than L years.
•(v) (a) Find E (Y), E (Y²) and Var(Y). (b) A random sample Y1, Y2, . , Yn is taken from Y - Exp(1). Write down the likelihood function I(1) and find the maximum likelihood estimator (MLE) of 1. (c) The lifetime T (years) of an electronic component follows ali exponential distribution Exp(1) (i) Find the lifetime L which a typical component is 60% certain to exceed. (ii) If five components are sold to a manufacturer, find the probability that at least one of them will have a lifetime less than L years.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:6) An exponentially distributed random variable Y has a probability density
function (pdf)
е л
y > 0
fy(y) =
y < 0
Exp(1).
(a) Find E (Y), E (Y²) and Var(Y).
written as Y
(b) A random sample Y,, Y,, .., Y, is taken from Y
the likelihood function l(A) and find the maximum likelihood estimator
(MLE) of 2.
(c) The lifetime T (years) of an electronic component follows aln exponential
distribution Exp(1)
Exp(1). Write down
(i)
Find the lifetime L which a typical component is 60% certain to
exceed.
(ii)
If five components are sold to a manufacturer, find the probability
that at least one of them will have a lifetime less than L years.
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