Summary of Probability Distributions
For Crystal Ball, all of these distributions can be used either from Crystal Balls Gallery (defined as assumption cells), or by explicitly writing the CB. function as a regular Excel formula. For @Risk, they can be ent
1
Lecture 1. Transformation of Random Variables
Suppose we are given a random variable X with density fX (x). We apply a function g to produce a random variable Y = g (X ). We can think of X as the input to a black box, and Y the output. We wish to nd the
Transformation and Expectation 1 Function of a random variable
Assume that X is a random variable with pmf/pdf fX , cdf FX . Denote the sample space of X by X . Then any function of X, say Y = g(X), is also a random variable. Examples: Y = X, X + 5, 3X 2
Summary of Probability Distributions of Discrete Random Variables
Name and parameter(s) of the distribution Binomial Bernoulli Negative Binomial Geometric B(n,p) n =1, p nb(r, p) r = 1, p pmf(*) n p( x ) = p x ( 1 p )n x x x = 0, 1, , n x 1 r xr p( x ) =
TRANSFORMATIONS OF RANDOM VARIABLES
1. INTRODUCTION 1.1. Denition. We are often interested in the probability distributions or densities of functions of one or more random variables. Suppose we have a set of random variables, X1, X2 , X3 , . . . Xn , with
Jordan Mitchell
1.16
Work
Not work
Men
15
23
38
Women
65
28
93
Total
80
51
131
a. The missing totals were 80,93,131
b. 39%
c. 61%
d. 70%
e. 61%
f. 50%
g. 11%
h. 560 women
1.30
We cannot conclude that pedestrians are safer because this is only a sample of
Jordan Mitchell
2.6
a. 12,20
b. 8 hours
c. 11
d. 11/50 22%
2.8
a. Detroit
b. Seattle
c. Left Skewed
2.30
Animals with outliers: African & Asian elephant 660,645
The humans data point would be the center of the distribution at 266 days
2.44
a. Midsize
b. T