Page 48 - Computational Statistics Handbook with MATLAB

34 Computational Statistics Handbook with MATLAB

• the time until the computer locks up,
• the time between arrivals of telephone calls, or
• the time until a part fails.

λ
The exponential probability density function with parameter is

(
f x λ) = λe – λx ; x ≥ 0; λ > . 0 (2.33)
;
The mean and variance of an exponential random variable are given by the
following:

1
EX[] = --- ,
λ

and

1
VX() = ----- .
λ 2

Exponential Distribution
2
1.8
λ = 2
1.6
1.4

1.2
f(x) 1
0.8
λ = 1
0.6
0.4
λ = 0.5
0.2
0
0 0.5 1 1.5 2 2.5 3
x

Exponential probability density functions for various values of λ .
URE
II
G
GU
GU
IG
F
F
F
U
FI
7
2.
7
7
7
2.
RE
2.
RE
2.
RE
© 2002 by Chapman & Hall/CRC