Name: _______________________
Class: __________
Date:_____________
Math SL: 23B Discrete Probability
Distributions
Review:
1. The diagram shows a circle of radius π cm. Find the perimeter and area of the shaded region.
1 radian
2. Let f (x) =
4 - x , x  4 and g (x) = x2, x 
(a) Find (g ◦ f ) (2);
(b) Find f −1(x);
.
(c) Write down the domain of f −1.
1
23B Discrete Probability Distributions
Today’s Objectives:
(1) to understand discrete probability distributions
Discrete Probability Distributions
A probability distribution for a discrete random variable is a list of each possible value of the
random variable and the probability that each value occurs. The probability that the variable X
takes value x is written as P(X = x) or sometimes just P(x) .
Probability distributions can be given as a table, graph, or sometimes even a function P(x).
Example 1: Let X be the random variable that represents the sum when two dice are tossed.
Tabulate the probability distribution for X.
The probability pi of any given outcome lies between 0 and 1, i.e. 0 £ pi £ 1.
n
If there are n possible outcomes then
åp
i
= ______ .
i =1
Or in other words: p1 + p2 + p3 + .... + pn = ____.
Example 2: Find k for the following probability distributions:
(a)
x
0
1
2
P(x)
0.3
k
0.5
(b)
P(x) = k (x + 2) for x = 1, 2, 3.
2
Example 3: A bag contains 5 blue and 3 green tickets. Two tickets are randomly selected without
replacement. We let X denote the number of blue tickets selected.
(a)
Find the probability distribution of X.
(b)
Suppose instead that three tickets are randomly selected without replacement. Find
the probability distribution of X for X = 0, 1, 2, 3.
Hmwk#51
23B Discrete probability distributions Pg. 633 # 1(b), 3(b), 4, 5, 6(b), 8, 11
Note: I would strongly recommend that you start to review for the next test. If you have
any questions regarding topics/concepts, be proactive and seek help. If you feel you need
more practice, then be proactive and COMPLETE more problems.
Continue researching a math exploration topic – find math involved.
3