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Chapter 8

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


Department
Spanish
Course Code
SPAN 101
Professor
Enrique Manchon
Chapter
8

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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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