Download Inverse

Introduction to
Probability & Statistics
Inverse Functions
Inverse Functions
 Actually,
we’ve already done this with the
normal distribution.
Inverse Normal
 Actually,
we’ve already done this with the
normal distribution.
0.1
x
3.0
X-m
Z=
s
3.38
x = m + sz
= 3.0 + 0.3 x 1.282
= 3.3846
Inverse Exponential
Exponential Life
2.0
1.8
1.6
F ( a ) = Pr{X  a}
a
- x
e
= 0  dx
=-e
- x a
0
=1- e -
a
Density
f ( x) =  e
- x
1.4
1.2
f(x)
1.0
0.8
0.6
0.4
0.2
0.0
0
0.5
1
a
1.5
2
Time to Fail
2.5
3
Inverse Exponential
F (x) = 1 - e
- X
F(x)
x
Inverse Exponential
F(x)
Suppose we wish to
find a such that the
probability of a
failure is limited to F(a)
0.1.
0.1 = 1 -
e
- a
ln(0.9) = -a
a
a = - ln(0.9)/
x
Inverse Exponential
Suppose a car battery is
governed by an exponential
distribution with  = 0.005. We
wish to determine a warranty
period such that the probability
of a failure is limited to 0.1.
a = - ln(0.9)/
= - (-2.3026)/0.005
= 21.07 hrs.
F(x)
F(a)
x
a