# MGMT 1050 Chapter Notes - Chapter 7: Continuous Or Discrete Variable, Random Variable, Standard Deviation

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Random variable – is a function or rule that assigns a number to each outcome of a

experiment

- Simply stated the value of a random variable is a numerical event

- There are two types of random variables: discrete and continuous

- A discrete random variable is countable

- A continuous random variable is not countable

Probability distribution – is a table, formula, or graph that describes the values of a random

variable and the probability of these values

- Probability distribution is important because it provides us information of a

population (probability distribution often represents population)

- The population mean is also called the expected value of x

Requirements for discrete random variable

1. 0 less than or equal to P(x) less than or equal to 1, for all x

2. P(x) = 1, all x

Binomial Experiment

1. The binomial experiment consists of a fixed number (n) of trials

2. The result of each trial is either: success or failure

3. The probability of success is always constant for each trial

4. Each trial is independent from other trials

If properties 2, 3, and 4 are satisfied, we say that each trial is a Bernoulli process. Adding

property 1 yields the binomial experiment. X is the random variable representing success, it

is called the binomial random variable. The binomial random variable is discrete

Cumulative probability – is when we wish to find the probability that a random variable is

less than or equal to

Continuous random variable

- Uncountable

- Values between whole numbers are possible

- Can be any value in an interval or in a collection of intervals

- Limited only by our ability to measure

- Anything that is measured rather than counting

- Need to treat it differently from discrete variable

- First, we cannot list the possible values because there is an infinite number of them

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