# Chapter 16 BVD

## 15 terms · Statistics: Modeling the World

### Random Variable

a confounding variable in which uncontrolled factors affected the dependent variable along with or instead of the independent variable

### Discrete Random Variable

random variable with either a fininte(whole) number value or a countable number.

### Continuous Random Variable

a variable that can take any numeric value within a range of values (range could be infinite, or bounded at either or both ends)

### Probability Model

a mathematical description of a random phenomenon consisting of a sample space and a way of assigning probabilities to events

### Expected Value

the sum of the values of a random variable divided by the number of values

### Variance

A measure of spread within a distribution (the square of the standard deviation).

### Standard Deviation

a measure of variability that describes an average distance of every score from the mean

### Changing a random variable by a constant

E(X ± c) = E(X) ± c
Var(X ± c) = Var(X)

E(aX) = aE(x)
Var(aX) = a²Var(X)
(NOT on green sheet)

### Adding or subtracting random variables

E(X ± Y) = E(X) ± E(Y) and if X and Y are independent, Var(X ± Y) = Var(X) + Var(Y) (The Pythagorean Theorem of Statistics). Remember Variances Add!!! (NOT on green sheet)

### To understand this chapter, first

be able to recognize random variables

### Then

understand that random variables must be independent in order to determine the variability of their sum of difference by adding variances

### Next

be able to find the probability model for a discrete random variable

### Fourth

know how to find the mean and the variance of a random variable

### Then,

know how to determine the new mean and standard deviation after adding a constant, multiplying a constant, or adding or subtracting two independent random variables

### Last,

be able to interpret the meaning of the expected value and standard deviation of a random variable in the proper context.