The document discusses probability distributions for discrete random variables, focusing on the frequency distribution that indicates how often specific outcomes occur. It provides examples using scenarios involving coin tosses to illustrate constructing frequency and probability distribution tables for the number of tails. Key values for random variables are determined based on the outcomes of tossing either three or four coins.

1. LC: illustrates a probability distribution for a discrete
random variable and its properties. M11/12SP-IIIa-4
Random Variables and
Probability Distributions

2. Frequency Distribution
Frequency tells you how often something
happened. The frequency of an observation tells
you the number of times the observation occurs in
the data.

3. Probability
Probability as a general concept can be defined as the
chance of an event occurring

7. 3. Construct the Frequency Distribution and Probability Distribution

8. Tossing Three Coins
Suppose three coins are tossed. Let Y be the random variable
representing the number of tails that occur. Find the values of
the random variable Y. Complete the table below.
TTT
TTH
THT
HTT
HHT
HTH
THH
HHH
3
2
2
2
1
1
1
0
The possible values of this random variable are 0, 1, 2, and 3.

9. Number of Tails (Y) Number of Occurrence
(Frequency)
Probability
P(Y)
0
1
2
3
1
3
3
1

10. Four coins are tossed. Let T be the random variable representing the number of tails that occur.
Find the values of the random variable T. Construct the probability distribution and frequency
distribution table.
Number of Tails (T) Number of Occurrence
(Frequency)
Probability
P(T)
TOTAL