# EC255 Lecture Notes - Lecture 3: Geometric Distribution, Standard Deviation, Binomial Distribution

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EC255 Week 3

4.8 REVISION OF PROBABILITIES: BAYES’ RULE

-a formula that extends the use of the law of conditional probabilities to allow revision of original

probabilities with new information

-The denominator of Bayes’ rule includes a product expression for every partition in the sample space Y,

including the event X itself

-The denominator is a collectively exhaustive listing of mutually exclusive outcomes of Y

-Staticians use Bayes’ rule to “revise” probabilities in light of new information

-Bayes’ rule provides a way of incorporating prior knowledge into our calculations. Or this reason, it can

be a valuable tool in decision making

5.1 DISCRETE VERSUS CONTINUOUS DISTRIBUTIONS

-A random variable is a variable that contains the outcomes of a chance experiment. Ex. 1 car, 2 cars, n

cars…

-The two categories of random variables are discrete and continuous

-A discrete random variable is if the set of all possible values is at most a finite or a count ably infinite

number of possible values. In most situations, discrete random variables product values that are

nonnegative whole numbers. Ex. If 6 people are randomly selected to be determined if they are left-

handed, it is discrete because the only possibilities are in the sample of 6: 0,1,2,3,4,5,6 – there cannot be

2.75 left-handed people

-Continuous random variables take on values at every point over a given interval. Ex. 8.67 seconds. Ex.

Measuring the supply of volume of liquid nitrogen in a storage tank.

-Ex. Discrete distributions – binomial distribution, poisson distribution, hyper geometric distribution

-Ex. Continuous distributions: uniform, normal, exponential, t, chi—square, F

5.2 DESCRIBING A DISCRETE DISTRIBUTION

-The histogram is probably the most common graphical way to depict a discrete distribution

Mean, Variance, and Standard Deviation of Discrete Distributions

-The measures of central tendency can be applied to discrete distributions to compute a mean, a

variance, and a standard deviation

5.2 BINOMIAL DISTRIBUTION

Assumptions of the binomial distribution:

-The experiment involves n identical trials

-Each trial has only two possible outcomes denoted as success or as failure

-Each trial is independent of the previous trials

-The terms p and q remain constant throughout the experiment, where the term p is the probability of

getting success on any one trial and the term q= l-p is the probability of getting a failure on any one trial

-Any single trial of a binomial experiment contains only two possible outcomes – these are labelled

success and failure

## Document Summary

A formula that extends the use of the law of conditional probabilities to allow revision of original probabilities with new information. The denominator of bayes" rule includes a product expression for every partition in the sample space y, including the event x itself. The denominator is a collectively exhaustive listing of mutually exclusive outcomes of y. Staticians use bayes" rule to revise probabilities in light of new information. Bayes" rule provides a way of incorporating prior knowledge into our calculations. Or this reason, it can be a valuable tool in decision making. A random variable is a variable that contains the outcomes of a chance experiment. The two categories of random variables are discrete and continuous. A discrete random variable is if the set of all possible values is at most a finite or a count ably infinite number of possible values. In most situations, discrete random variables product values that are nonnegative whole numbers.