2. Lesson Objectives:
Illustrate a probability distribution for a discrete
random variables and its properties.
Compute probabilities corresponding to a given
random variable.
Construct the probability mass function of a
discrete random variable and its corresponding
histogram.
3. Probability Distribution
A discrete probability distribution or a
probability mass function consists of the
values a random variable can assume and
corresponding probabilities of the values.
4. Example:
Suppose three coins are tossed. Let Y be
the random variable representing the
number of tails that occur. Find the
probability of each of the values of the
random variable Y.
5. Possible Outcomes
Values of the Random Variable
Y (Number of tails)
TTT 3
TTH 2
THT 2
HTT 2
HHT 1
HTH 1
THH 1
HHH 0
6. There are four possible values of the random variable Y
representing the number of tails. These are 0, 1, 2, and 3. Assign
probability values P(Y), to each value of the random variable.
• There are 8 possible outcomes and no tail occurs once, so the
probability that we shall assign to the random variable 0 is
1
8
.
• There are 8 possible outcomes and 1 tail occurs three times, so
the probability that we shall assign to the random variable 1 is
3
8
.
• There are 8 possible outcomes and 2 tail occurs three times, so
the probability that we shall assign to the random variable 1 is
3
8
.
• There are 8 possible outcomes and 3 tail occurs once, so the
probability that we shall assign to the random variable 3 is
1
8
.
7.
8. Properties of Probability Distribution
1. The probability of each value of the random
variable X must be between 0 and 1 or equal
to 0 or 1. In symbol, we write it as 𝟎 ≤
𝑷(𝑿) ≤ 𝟏.
2. The sum of the probabilities of all values of
the random variable X must be equal to 1. In
symbol, we write it as 𝑷 𝑿 = 𝟏.
