# SPAN 101 Chapter Notes - Chapter 8: Unimodality, Probability Distribution, Geometric Probability

by OC2168805

Department

SpanishCourse Code

SPAN 101Professor

Enrique ManchonChapter

8This

**preview**shows half of the first page. to view the full**3 pages of the document.**CH 8 RANDOM VARIABLES AND PROBABILITY MODELS

Expected value of a discrete random variable is found by multiplying each possible

value of the random variable by the probability that it occurs and then summing all

those products:

E(X)= Ex P(x)

Changing a random variable by a constant:

E(X +- c) = E(X) +- c

Var (X +- c) = Var (X)

SD (X +- c) = SD (X)

Multiplying:

E(aX) = aE(X)

Var (aX) = a2 Var(X)

SD (aX) = |a| SD (X)

Addition Rule for expected values of random variables: the expected value of the

sum/ difference of random variables is the sum/differences of their expected values

E( X +- Y) = E(X) +- E(Y)

Addition rule for Variances of Independent random variables: the variance of the

sum or difference of 2 independent variables is the sum of their individual

variances:

Var( X +- Y) = Var(X) + Var(Y) ; if X and Y are independent

• The expected value of the sum of two random variables is the sum of the

expected values

• The expected value of the difference of two random variables is the

difference of the expected values

• If the random variables are independent, the variance of their sum or

difference is always the sum of the variances

Bernoulli trail:

• If there are only two possible outcomes for each trail

• Probability of success, denoted p, is the same on every trail

• The trails are independent

• Geometric probability model: completely specified by one parameter, p, the

probability of success

o p = probability of success

o q = 1-P

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