Page 150 - Probability Demystified

CHAPTER 8 Other Probability Distributions 139

4. A coin is tossed until 4 heads are obtained. What is the expected
number of tosses?
5. A service station operator gives a scratch-off card with each fill up
over 8 gallons. On each card is one of 5 colors. When a customer gets
all five colors, he wins 10 gallons of gasoline. Find the average num-
ber of fill ups needed to win the 10 gallons.

ANSWERS

3 3 1 9
1. ¼
4 4 4 64
2 1 1 1 1
2. p ¼ ¼ ; ¼ ¼ 1 ¼ 1 3 ¼ 3
6 3 p 1 3
3
3 1
3. ¼ 3 ¼ 3 6 ¼ 18
1 6
6
4 1
4. ¼ 4 ¼ 4 2 ¼ 8
1 2
2
5 5 5 5 5
5. 1 þ þ þ þ ¼ 11 , i.e. 12 fill ups
4 3 2 1 12

The Poisson Distribution

Another commonly used discrete distribution is the Poisson distribution
(named after Simeon D. Poisson, 1781–1840). This distribution is used when
the variable occurs over a period of time, volume, area, etc. For example,
it can be used to describe the arrivals of airplanes at an airport, the number of
phone calls per hour for a 911 operator, the density of a certain species
of plants over a geographic region, or the number of white blood cells on a
fixed area.
The probability of x successes is
x
e
x!
where e is a mathematical constant 2.7183 and is the mean or expected
value of the variable.