Conditional Probability
Conditional probability still applies:
P(T<t1|T<t2) = P(T<t1T<t2) / P(T<t2)
P(T<t1|T>t2) = P(T<t1T>t2) / P(T>t2)
Generic Distribution
Generic Distribution
f(t) = 2t/15
for 1 < t < 4
Calculate and plot F(t)
Calculate
P(t < 2.5)
P(2.

Geometric Probability Distribution - Background
Special case of Negative Binomial when r =1
First (y-1) attempts result in failure and are followed by first success
p(y) = (q)(y-1)p
y = number of trials until first success
Geometric Distribution
Mean and

Exercise
= 2 calls/hour
Find probability there will be 6 or fewer calls in 4 hour time period
4 hour period becomes the interval of interest
l=t = (2) (4) = 8 8 calls per 4 hour period
Find P(Y < 6)
Exercise (contd)
= 2 calls/hour
Find probability there

Continuous Probability Distributions
Chapter 5
Consider
Daily Rainfall at location X
Waiting time, W, at a traffic light
X and W take on an uncountably infinite number of values
X and W are continuous random variables
Consider
Let s be strength of a steel

4.10 Poisson
Count number of occurrences in a time interval or geographic area
Examples
Number of new jobs submitted to computer any one minute
Number of fatal accidents per month in factory
Assumptions
Extension of binomial under limiting assumptions, wh

Continuous Uniform Random Variable
Uniform Probability Distribution
pdf
f(t) = 1/(b-a)
= (a + b)/2
a< t < b and 0 elsewhere
2 = (b-a)2/12
Find F(t) in general (remember area)
cdf F(t) = 0
for t < a
= (x-a)/(b-a)
=1
for a< t < b
for t > b
Normal Probabili

1. The mean running time for a group of athletes for 0.25 mile is 25 seconds with a standard
deviation of 9.2 seconds. If in a race 10 athletes run, each of them running 0.25 miles
consecutively, what is the probability that they will finish less than 4 m

1. An auto part is produced by a sequence of similar machines. Processing time of a
single machine has a mean of 10 sec and standard deviation of 2.3 sec. If the
production line has 35 consecutive such machines, what is the probability that total
time for