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Unit 6
Random
Variables
6.2B
Combining Random Variables
(with the help of MEGA Algebra)
 Describe the measures of center
(mean) and spread (stdev) that
result from combining two or more
random variables
(Combining = adding/subtracting!)
Speed Dating
At a speed-dating event, women sit in a circle, and
each man spends about 5 minutes getting to know
a woman before moving on to the next one. What
is the probability that the man is taller than the
woman in a randomly selected speed-dating
couple?
Mythical College Main Campus
X
12
13
14
15
16
17
18
P(X) 0.25 0.10 0.05 0.30 0.10 0.05 0.15
Mythical College Downtown Campus
Y
12
13
14
15
16
17
18
P(Y) 0.35 0.15 0.10 0.20 0.05 0.05 0.10
Consider the random
variables X and Y
each with its own
measures of center and
spread.
Variable
Mean
X
𝜇𝑋
Y
𝜇𝑌
Variance
Stdev
𝜎𝑋
2
𝜎𝑋
𝜎𝑌
2
𝜎𝑌
Now consider the NEW
random variable formed when
we add(or subtract) values of
X and Y.
Let’s call this variable X ± Y.
Let’s find the mean and
standard deviation of X ± Y.
First we will find the mean
𝜇𝑋±𝑌
𝜇𝑋±𝑌 = 𝜇𝑋 ± 𝜇𝑌
Yay. Not so bad.
Next we will find 𝜎𝑋±𝑌
by finding the variance
2
𝜎𝑋±𝑌
𝜎𝑋±𝑌
2
2
= 𝜎𝑋 +𝜎𝑌
2
NOTE#1 This is only true
when X & Y are independent
NOTE#2 When independent,
variances add, even when we
subtract to get our new var.
EX 1) Let’s take a random American
hetero couple, calculate their
heights and subtract. The NEW
random variable formed would be
the difference M ‒ F.
Find the mean and standard
deviation of M ‒ F.
EX 2) Take two random American
women, calculating their heights
and subtract. The NEW random
variable formed would be the
difference F1 ‒ F2.
Find the mean and standard
deviation of F1 ‒ F2.
Roulette Revisted
 Suppose
the gambler plays two games of
roulette, still keeping the $1 bet each time.
What can we say about the total gain (or loss)
from playing two games?