BSB123 Lecture Notes - Lecture 4: Statistical Hypothesis Testing, Statistical Inference, Null Hypothesis
Data Analysis – Discrete Probability Distributions
- Probability Distributions:
oRandom Variable
A variable that assumes numerical values according to the random outcome
of an experiment
Examples
Number obtained when rolling a die
Number of students who turn up to class each week
Temperature in any given day
Number of job vacancies advertised in any given day
Number of customers in a queue
Discrete random variables
Have a finite (or countable finite) number of possible values
Continuous random variables
Have infinitely many possible values
oProbability Distributions
Describes the probability that the variable (x) will take on for each of its
possible values
oExpected Value
Mean of a discrete probability distribution
The weighted average of all possible outcomes associated with the random
variable
Formula is n*
- Binomial Distribution
oIn each experiment there are only two possible outcomes – success and failure
oUseful when dealing with qualitative data
oIncludes the No. of trials (n), the probability of success (), and the No. of successes
(X)
oCharacteristics
There must be a fixed number of trials
There must be only two possible outcomes
Each trial of the experiment is independent of any other
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Document Summary
A variable that assumes numerical values according to the random outcome of an experiment. Number of students who turn up to class each week. Number of job vacancies advertised in any given day. Have a finite (or countable finite) number of possible values. Have infinitely many possible values: probability distributions. Describes the probability that the variable (x) will take on for each of its possible values: expected value. The weighted average of all possible outcomes associated with the random variable. There must be a fixed number of trials. Each trial of the experiment is independent of any other. The probability of success is constant: binomial random variable. Number of successes in n trials of a binomial experiment: binomial probability distribution. Probability distribution of a binomial random variable: use binomial tables to calculate probabilities, expected payout. Expectation = average in the long run of large number.
