1. 7.1: Discrete and Continuous Random Variables
Ch. 7 Random Variables
7.1: Discrete and Continuous Random Variables

2. Random Variable-
variable whose value is a numerical outcome of a random phenomenon; usually denoted with capital letters (X or Y)
Discrete Random Variables-
a countable number of possible values

3. For Discrete Random Variables
Probability Distribution: all the possible values with their corresponding probabilities
All probabilities pi must be between 0 and 1.
The sum of all probabilities

4. Example
Imagine selecting a U.S. high school student at random. Define the random variable X = number of languages spoken by the randomly selected student. The table below gives the probability distribution of X, based on a sample of students from the U.S. Census at School database. (a) Show that the probability distribution for X is legitimate. (b) Make a histogram of the probability distribution. Describe what you see. (c) What is the probability that a randomly selected student speaks at least 3 languages? More than 3?
Languages: 1 2 3 4 5
Probability:
0.630
0.295
0.065
0.008
0.002

5. Let’s Play a Game! Rules: 1.) Winner receives $100.
2.) Use the RAND function on your calculator.
3.) You have 30 seconds to try and get the number
Good luck!

6. Game Debrief: What is the sample space for this game?
P(X= )
P(X>0.75)

7. Continuous Random Variable
Takes all values in an INTERVAL of numbers
Probability Distribution-
is described by a density curve (Area=1)
area under the curve is equal to the probability for that event

8. Game Example: P(X<0.2) P(X=0.2)
Every individual outcome has a probability of _______ in a continuous probability distribution.

9. Example: 2 4 .2 .4
A.) Verify that this is a legitimate probability distribution.
B.) P(X>3)
C.) P(X<3)
D.) P(X=3)

10. Normal Distribution- is a probability distribution
p=proportion of entire population = proportion of a sample The population proportion who jog is p=0.15. A SRS of 1500 adults asked, “Do you happen to jog?” The statistic is a random variable normally distributed with p=0.15 and =0.0092

11. …continued