Chapter 16

Question 1

random variable

Answer 1

a random variable assumes any of several different numeric values as a result of some random event. Random variables are denoted by a capital letter such as X.

Question 2

discrete random variable

Answer 2

a random variable that can take one of a finite number^3 of distinct outcomes is called a discrete random variable.

Question 3

continuous random variable

Answer 3

a random variable that can take any numeric value within a range of values is called a continuous random variable. The range may be infinite or bounded at either or both ends

Question 4

probability model

Answer 4

the probability model is a function that associates a probability P with each value of a discrete random variable X, denoted P(X=x), or with any interval of values of a continuous random variable.

Question 5

expected value

Answer 5

theoretical long-run average value, the center of its model. Denoted μ or E(X), it is found (if the random variable is discrete) by summing the products of variable values and probabilities:

μ= Ε(Χ)= ΣxP(x)

Question 6

variance

Answer 6

the expected value of the squared deviation from the mean. For discrete random variables, it can be calculated as:

σ^2= Var(X)=Σ(x-μ)^2P(x)

Question 7

standard deviation

Answer 7

describes the spread in the model, and is the square root of the variance:

σ=SD(X)= √Var(X)

Question 8

changing a random variable by a constant

Answer 8

E(X + or - c) = E(X) +or- c
E(aX)= aE(X)
Var(X + or - c) = Var(X)
Var(aX)= a^2Var(X)

Question 9

adding or subtracting random variables

Answer 9

E(X + or - Y)=E(X) + or - E(Y)
if X and Y are independent, Var(X = or - Y)= Var(X) + Var(Y)
(the Pythagorean Theorem of Statistics)