Download Joint Probability Distributions

Joint Probability Distributions

Just like…..

Except….

One variable is…

One variable is…
Example:
Y
X
1
2
3
Total
1
0.32
0.14
0.19
0.65
2
0.17
0.06
0.12
0.35
Total
0.49
0.2
0.31
1
Let’s look at X and Y separately:
For X, what is the probability distribution?
X
P(X)
For Y, what is the probability distribution?
Y
P(Y)
Questions:
1. P(X=1) =
2. P(Y=2|X=1) =
3. P(Y=2 ∩ X=1) =
4. P(Y=3) =
Now what if we have the following independent 2 variables:
X
P(X)
1
0.25
Y
P(Y)
2
0.74
1
0.18
2
0.42
3
0.4
We want to combine the two together, in a joint probability distribution:
1
2
3
Total
1
2
Total

Write the…

To fill out the cells of the distribution, just…

Why can we just multiply the probabilities from the row and column totals
to get the probability of the cell?
AP Statistics
Section 4.4 – Joint Probability Distributions
1. A study was made to compare year in high school with preference for vanilla or
chocolate ice cream with the following joint probability table.
Freshman (X=1)
Sophomore (X=2)
Junior (X=3)
Senior (X=4)
Vanilla (Y=1)
.16
.19
.14
.17
Chocolate (Y=2)
.08
.10
.07
.09
a. What is the probability distribution for Y?
b. Find P(X=1, Y=2) (this is the same thing as P(X=1 ∩ Y=2)
c. Find P(Y=1X=3)
2. Following are the probability distributions for the random variables X and Y.
x
1
2
3
P(x)
.2
.5
.3
y
1
2
P(y)
.4
.6
a. If X and Y are independent random variables, what is their joint probability
table?
3. Following are parts of the probability distributions for the random variables X and Y.
If X and Y are independent and the joint probabilities P(X=1 and Y=1) = .06 and
P(X=2 and Y=2) = .1, what is P(X=3 and Y=3)?
x
1
2
3
P(x)
?
.4
?
y
1
2
3
P(y)
.3
?
?