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.

Contents

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

[1]

  • 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

[2]

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]

End

This is the end of this topic. Click here to go back to the main subject page for Business and Economic Statistics.

References

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

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