1. RANDOM VARIABLES Random variable:
A variable whose numerical value is determined by the outcome of a random experiment
Discrete random variable
A discrete random variable has a countable number of possible values.
Example
Number of heads in an experiment with 10 coins
If X denotes the number of heads in an experiment with 10 coins, then X can take a a value of 0, 1, 2, …, 10

2. RANDOM VARIABLES
Other examples of discrete random variable: number of defective items in a production batch of 100, number of customers arriving in a bank in every 15 minute, number of calls received in an hour, etc.
Continuous random variable
A continuous random variable can assume an uncountable number of values.
Examples
The time between two customers arriving in a bank, the time required by a teller to serve a customer, etc.

3. DISCRETE PROBABILITY DSTRIBUTION
Discrete probability distribution
A table, formula, or graph that lists all possible events and probabilities a discrete random variable can assume
An example is shown below:
Discrete Probability Distribution
0.75
0.5
Probability
0.25 HH HT TT
Event

4. CONTINUOUS PROBABILITY DSTRIBUTION
Continuous probability distribution
Similar to discrete probability distribution
Since there are uncountable number of events, all the events cannot be specified
Probability that a continuous random variable will assume a particular value is zero!!
However, the probability that the continuous random variable will assume a value within a certain specified range, is not necessarily zero
A continuous probability distribution gives probability values for a range of values that the continuous random variable may assume

5. CONTINUOUS PROBABILITY DSTRIBUTION
f(x) z

6. CONTINUOUS PROBABILITY DSTRIBUTION
f(x) z

7. REVISIT SIMPLE RANDOM SAMPLING
In Chapter 5, a simple random sample of 10 families is chosen from a group of 40 families.
40 Random numbers are generated
Each random number is between 0 and 1 (not including 1)
Excel RAND() function is used to generate each random number.

8. REVISIT SIMPLE RANDOM SAMPLING
What is the average of the random numbers generated?
What is the variance of the random numbers generated?
What is the standard deviation of the random numbers generated?

9. REVISIT SIMPLE RANDOM SAMPLING
Plot a histogram with all the random numbers, and comment on the distribution of the random numbers.