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Chapter 7

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


Department
Management
Course Code
MGMT 1050
Professor
Olga Kraminer
Chapter
7

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Chapter 7 Notes
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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