Download Chapter 4 Discrete Probability Distributions

Chapter 4
Discrete Probability Distributions
4.1 Probability Distributions
I. Random Variables
• A random variable x represents a
numerical value associated5with
each outcome of a probability
experiment.
There are two types of
random variables
• Discrete random variables
have a finite or countable
number of possible
outcomes that can be
listed.
• (Whole numbers)
• Continuous random
variables have an
uncountable number of
outcomes, represented by
an interval on the number
line.
• (Decimals and fractions)
• Example & TIY #1 (p173)
II. Discrete Probability Distributions
• A discrete probability distribution lists each
possible value that a random variable can
assume, together with its probability. And
must satisfy…
– 0 ≤ P(x) ≤ 1
– ∑ P(x) = 1
Because probabilities represent relative frequencies
we can use a relative frequency histogram
to display our data.
Constructing a Discrete Probability Distribution
1. Make a frequency distribution for the
possible outcomes.
2. Find the sum of the frequencies.
3. Find the probability of each possible
outcome by dividing its frequency by the sum
of the frequencies.
4. Check that each probability is between 0 and
1 and the sum is 1.
Examples
• Example 2 (p174)
• TIY#2
More Examples
• Example 3 (p175)
• Example 4 (p175)
• TIY #3
• TIY#4
HW: p179-181 # 8-26 even
& #28 (a) ONLY
4.1 continues…
III. Mean, Variance & Standard Deviation
• Mean: µ = ∑ x ∙ P(x)
– Represents theoretical average and sometimes is
not a possible outcome.
– Round 1 decimal place further than your data.
(Finish #28 from hw as example)
• Standard Deviation
– Variance: σ2 = ∑ (x - µ)2 ∙ P(x)
– St. Dev. : σ = √ σ2
IV. Expected Value
• Same formula as the mean E(x) = ∑ x ∙ P(x)
• E(x) = 0 means it’s a fair game or the break
even point
• HW: p181-183 #30-38even