AP Statistics
Chapter 6 Assignments
Random Variables
*Assignments are subject to change
Date Section
6.1
6.2
6.3
Topic
Discrete and Continuous Random Variables
Transforming and Combining Random
Variables
Binomial and Geometric Random Variables
Chapter 6 Review
AP Set 6
Assignment
Pg. 353 #1,5-9 odds, 13 14, 18, 19, 23, 25
Pg. 356 27-30 Pg. 378 #37, 39-41, 43,
45,49, 51, 57-59, 63
Pg. 381 #61, 65, 66
Pg. 403 # 69-89 odds
Pg. 409 # T6.1 – 6.10
Discrete Random Variables
Random phenomenon has individual outcomes that are not able to be predicted, however, the distribution of
these outcomes has a regular pattern.
 Mean:  X  x1 p1  x2 p2  ...  xk pk

 Variances:  X2  ( x1   X )2 ( p1 )  ( x2   X )2 ( p2 )  ...  ( xk   X ) 2 ( pk )

Probability distribution table

Probability histogram

Mean of a discrete random variable

Standard deviation of a discrete random variable

Combining Random variables
 Rule for Means: abx  a  b X

Rule for Variances:
 x  y   X  Y
*Independence is a requirement
 a2bx  b 2 X2


 X2 Y   X2   Y2

 X2 Y   X2   Y2
Part 3 Binomial and Geometric Distributions
Binomial
 Symbols B(n, p)
 Symbol for Mean
 Symbol for Standard deviation
 Capital X and lower case x
 When a Binomial approaches a Normal
 Website applet
Binomial Distributions
Conditions of a Binomial Distribution
1. Observations must be either "success" or "failure"
2. All observations must be independent.
3. The probability of success, p, must be the same
for all observations.
4. There must be a fixed number of observations.
Formula:
nC r
pr (1 - p)n - r
Secret Shortcut: Binomial pdf (n,p,r)
Arguments are alphabetical
What this finds: Probability of "r" successes in "n" trials
with probability "p"
Another Secret Shortcut: Binomial cdf (n,p,r)
What this finds: Probability of getting AT MOST "r"
successes in "n" trials with probability "p"
Mean & Standard Deviation of Binomial Random
Variable:
 = np
=
np(1  p)
Geometric Distributions
Conditions of a Geometric Distribution
1. Observations must be either "success" or "failure"
2. All observations must be independent.
3. The probability of success, p, must be the same
for all observations.
4. The variable of interest is the number of
observations required to get the first success.
Formula:
p1 (1 - p) n - 1
Secret Shortcut:
Geometric pdf (p,r)
What this finds: Probability of 1st success on trial "r"
with probability "p"
Another Secret Shortcut: Geometric cdf (p,r)
What this finds: Probability that it takes AT MOST "r"
trials, with probability "p
Another important formula:
P(x>n) = (1-p)n probability that it takes more than n
trials to see first success
Mean of Geometric Random Variable
 = 1/p