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

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This article is a topic within the subject Business & Economic Statistics.


Required Reading

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
    • ECON120345.jpg
      • Where n = # of trials and x = is the # of successes
    • Mean = μ = np
    • Variance = σ^2 = np(1-p) (Standard Deviation = σ)

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.

ECON12035Wi.png [3]


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Textbook refers to Gerald Keller (2011), Statistics for Management and Economics (Abbreviated), 9th Edition,.

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