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Unformatted text preview: and mean of T. By deﬁnition of the exponential distribution
with parameter λ = 0.01, the pdf of T is
fT (u) = (0.01)e−(0.01)u for u ≥ 0
0
for u < 0, where the variable u is a measure of time in seconds. The mean of an exponentially distributed
1
random variable with parameter λ is λ , so E [T ] = 0.1 = 100.
01
[T
T
The waiting time in minutes is given by S = 60 . By the linearity of expectation, E [S ] = E60 ] =
100
60 = 1.66 . . . . That is, the mean waiting time is 100 seconds, or 1.666 . . . minutes. By the scaling
formula with a = 1/60 and b = 0,
fS (v ) = fT (60v )60 = (60)(0.01)e−(0.01)60v = (0.6)e−(0.6)v for v ≥ 0
0
for v < 0, where v is a measure of time in minutes. Examining this pdf shows that S is exponentially distributed with parameter 0.60. From this fact, we can ﬁnd the mean of S a second way–it is one
over the parameter in the exponential distribution for S, namely 116 = 1.666 . . . , as already noted.
. Example 3.6.3 Let X be a uniformly distributed random variable on some interval [a, b]. Find
−µ
t...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
 Spring '08
 Zahrn
 The Land

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