Math 302.102 Fall 2010
Assignment #6
This assignment is due at the beginning of class on Wednesday, November 10, 2010.
1.
The exponential distribution has an important property that uniquely characterizes it among
continuous distributions, the
lack of memory property
, also known as the
memoryless property
.
Suppose that
X
∼
Exp(
λ
) and let
s >
0 and
t >
0 be real numbers. Show, by a direct calculation,
that
P
{
X > t
+
s

X > t
}
=
P
{
X > s
}
.
In other words, start with the object on the left side of the equality, manipulate it using the defini
tion of conditional probability, and arrive at the expression on the right side of the equality. What
this identity says is that if the lifetime of a component follows an exponential distribution, then
the probability that the component’s lifetime is at least
s
+
t
given that the component’s lifetime
is at least
t
is simply the probability that the component’s lifetime is at least
s
. An alternative
interpretation is the following. Suppose you are standing in line and the amount of time in minutes
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 Spring '08
 ISRAEL
 Math, Probability, Probability theory, Exponential distribution, density function, memoryless, 2 2 m

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