Chapter 7

1. Discrete and Random Variables

a. Random Variables

i. Must take on a numerical value

b. Discrete Random Variables

i. Countable items.  Finite number of possibilities

that have a probability assigned to them.

c. Continuous Random Variable

i. Infinite number of possibilities.  Probability for

such events is done over an interval rather than

an individual number.

ii. Area under any density curve is equal to one.

The area will now become the probability.

iii. Use of the normal curve.

2. Mean and Variance of Random Variables

a. The mean for any random variable is also called the

Expected Value.  In other words the average “mu” is

what is expected out of the probability distribution.

b. The variance or standard deviation squared is the

amount of variation the data contains within the

distribution.

3. Rules for the Mean and Variance

a. Mean

i. If X is a random variable then, (see pg. 418)

ii. If X and Y are random variables then (see pg.

418)

b. Variance

i. If X is a random variable then, (see pg. 420)

ii. If X and Y are random variables and X and Y are

independent of each other then, (see pg. 420)

iii. If X and Y are random variables and X and Y are

not independent of each other then, (see pg.

421) where rho is the correlation coefficient

between X and Y.

AP Statistics

Syllabus

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