Download Rules for combining and manipulating Means

Rules for combining and manipulating Means
X and Y = R.V.’s
a and b = fixed numbers
Rule for multiplication and addition of one variable:
Rule for Combining X and Y together:
Example:
1) Random variable X has mean of 6.2. Find the mean if we divide by 12 and
add 3.
2) Random variable Y has mean of 3.4. Find the mean of X + Y.
Rules for combining and manipulating Std. Deviations
X and Y = R.V.’s
a and b = fixed numbers
Notes:
 Variance =

ALWAYS…
Rule for multiplication and addition of one variable:
 Adding or subtracting a constant to a variable…
Rule for Combining X and Y together:
Example:
1) Random Variable X has σ = 3.1.
Random Variable Y has σ = 1.4.
Find:
σx+y =
σx-y =
σ2x+3 =
σ3x+y-4 =
AP Statistics
Section 4.4 – Rules for Means and Variances
1. Suppose that X is a random variable with  X  10 and  X = 2. Find the following:
a.  5 X
b.  X 3
c.  5 X 3
d.  5 X
e.  X 3
2. Suppose that X is the random variable from above, and that Y is independent from X
with Y  15 and  Y  3 . Find the following:
a.  X Y
b.  X 3Y
c.  X Y
d.  X Y
e.  5 X  2Y
3. Suppose the mean SAT verbal score is 425 with standard deviation 100, while the
mean SAT math score is 475 with standard deviation 100. What can be said about
the mean and standard deviation of the combined math and verbal score?
4. The Graduate Record examination (GRE) has three components: math, verbal, and
analytical (all scored on a scale from 200 to 800). Suppose that the mean and
standard deviation for math are 490 and 95, the mean and standard deviation for
verbal are 476 and 98, and for analytical the mean and standard deviation are 510 and
105. Find the mean and standard deviation for the combined score of all three
examinations (assume the scores are independent).