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AP STATISTICS
Section 7.1 Random Variables
Objective: To be able to recognize discrete and continuous
random variables and calculate probabilities using them.
A Random Variable is a variable whose value is a
numerical outcome of a random event.
Denoted using capital letters: X, Y, …
Ex. X = sum of 2 dice
A discrete random variable has a countable number of
possible outcomes.
A probability distribution is a table that assigns probabilities
to outcomes of a discrete random variable.
General Probability Table:
X=𝒙𝒊
𝒙𝟏
𝒙𝟐
…
𝒙𝒏
P(X=𝒙𝒊 )
𝑝1
𝑝2
…
𝑝𝑛
**
Last row is optional. Only include it if asked to do so.
F(X=𝑥𝑖 ) is the cumulative density function.
F(X=𝑥𝑖 ) = P(X ≤ 𝑥𝑖 )
Every Probability Distribution must meet 2 requirements:
1. Every 𝑝𝑖 is between 0 and 1.
2. The 𝑝𝑖 = 1
Ex. Create the probability distribution for the random
variable X where X = the sum of two dice. Then answer
the following questions.
(X=𝑥𝑖 )
P(X=
𝑥𝑖 )
Find P(X=7 or 11) =
Find P(X = 2 or 3 or 12)=
The best way to display a probability distribution is through
the use of a __________________________.
Ex. Create a probability distribution for the random variable
X where X = the number of times a head is observed when
a coin is tossed 3 times.
REVIEW DENSITY CURVES:
1.
2.
Z-SCORES:
A continuous random variable takes on all values of that
random variable in an interval of numbers.
• The probability distribution of a continuous random
variable is described by a density curve.
• The area under the curve represents the probability of the
said event occurring.
• Continuous random variables are measured while
discrete are counted.
Ex. Let X~U(0,2)
a. Sketch this density curve.
b. Find P(X < 1)
c. Find P(X ≤ 1)
d. Find P(0.5 < X < 1.6)