Quantitative Study Guide

PROBABILITY (module 4 & 5)

Probability for a discrete variable

Probability for a discrete variable=chance of the discrete variable taking on a particular value, expressed as a percentage

These can be estimated by experiments or observations, called empirical probability.

Explained in excel

Probability Distribution: A Tabulated view of the uncertain behavior of a discrete random variable

Cumulative Distribution: Another Tabulated view of the uncertain behavior of a discrete random variable

Expectation of a variable: A weighted average taking into account the probability.

Difference between DV and Random Variable.

***We control a decision variable, and so we can stop being uncertain about it any time we want to make the decision. Random variables are used in decision-analysis models only to represent quantities that we do not know and cannot control.

Let us use the variable X to represent number of dots from tossing a fair die.

a. Tabulate the probability and cumulative distribution of X

X=xi 1 2 3 4 5 6

Probability Distribution P(X=xi) 1/6 1/6 1/6 1/6 1/6 1/6

Cumulative Distribution P(X4), P(X=1.5), P(X 1 *1 * .00109 = .0011

c. at least 2 of the 3 orders will be filled correctly?

x=2|n=3| π=.897

3!/2!(3-2)! * .8972(1-.897)3-2 => 6/2 * .8046(.103)1 => 3*.8046(.103) = .2486 then add answer from A

.2486+.7217 = .9703 adding answer from a and the first part of this answer since it says at least 2

d. what are the mean and standard deviation of the binomial distribution used in (a) through (c)? interpret these values

µ=E(x) = nπ so this means .897*3 = 2.691

σ =√σ2 => √nπ(1-π) =>√3*.897(1-.897)=> √.2772 = .5265

Poisson Distribution

P(X=x|λ) = e-λ λx / x!

Where P(X=x|λ) = probability that X=x events in an area of opportunity given λ

λ = expected # of events

e = mathematical constant approximated by 2.71828

x = number of events (x = 0,1,2,….,∞)

Problem 5.32 – The quality control manager of Marilyn’s Cookies...