# Topic 5 - Discrete (Binomial Distribution) And Continuous Random Variables (Probability Density Function)

## Contents

Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition, pp. 264-270 + Previous Chapter.

## Discrete Variables

All the relevant information on discrete variables can be found in the previous topic here.

## Binomial Distribution

• Requirements
• Fixed number of trials ‘n’
• 2 Possible outcomes, success/failure
• Success = p & failure = 1-p
• The trials are independent
• Each trial is a Bernoulli process
• The RV of a binomial experiment is the number of successes in ‘n’ number of trials - The binomial random variable
• Binomial Random Variable

Lets say we will toss a coin 10 times. The probability of getting 4 heads is equal to 10C4(0.5)^4(0.5)^(6).

## Continuous Probability Distributions – Chapter 8

### Probability Density Functions

A continuous Random Variable (RV) has an uncountable number of values. The probability of each individual value is virtually 0. Thus, we can only determine the probability of a range of values.

More on this here.

#### Probability Distribution Function Rules

• F(x) => 0 for all x between a & b (on the x axis)
• Total area between a & b = 1

#### Uniform Probability Density Functions

The function is uniformly distributed, meaning that the point on the y axis, F(x) = 1 / (b-a). (Assuming 'a' & 'b' are the 2 numbers on the x axis - as shown in the picture below).

Lets assume I will get to uni sometime between 8 and 9am (uniformly distributed). The probability of arriving at exactly 8:25 is virtually 0. The chance of arriving between 8:25 and 8:30 is 5/60 = 1/12.

## End

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