Distributions & Hypothesis Testing

During our everyday life we frequently conduct random experiments, without necessarily being aware of it. For example, if we are buying a new car, we might test drive say five cars, and judge each car as ‘suitable’ or ‘unsuitable’. When an experiment has a quantitative feature, we can associate a number with each outcome of the experiment. The outcome of the experiment defines a random variable x.


This course is about random variables, probability distributions, the testing of hypotheses, and confidence levels. Understanding these concepts is essential in the financial world, particularly in option pricing and risk measurement. The course covers the types of random variable and the probability distributions that each follows. It also provides information about the parameters of the distributions. It introduces the concept of hypothesis testing and confidence levels, and also looks at situations where the use of one-tailed or two-tailed confidence levels must be determined.


    On completion of this course, you will be able to:

    Describe how a random variable is distributed, and compute the expected value and standard deviation/variance of a random variable

    Test hypotheses about the expected value of a variable and evaluate the likelihood of a certain event with a specified probability


    Topic 1: Random Variables

    Probability Distribution of a Discrete Random Variable

    Probability Distribution of a Continuous Random Variable

    Mean and Standard Deviation of a Discrete Probability Distribution

    o Mean

    o Standard Deviation

    o Variance

    Binomial Distribution

    Binomial Distribution – Probability

    Binomial Distribution – Formula

    Mean, Variance, and Standard Deviation for a Binomial Random Variable

    Continuous Probability Distributions

    The Normal Distribution – Formula

    The Normal Distribution – Properties

    Normal Random Variables

    The Standard Normal Distribution

    Determination of Normal Distribution

    Other Continuous Probability Distributions

    o Uniform Probability Distribution

    o Lognormal Probability Distribution

    o Exponential Probability Distribution

    Topic 2: Hypothesis

    Hypothesis Testing

    Confidence Levels

    Rejection and Non-rejection of Hypothesis

    One-Tailed Confidence Level

    Two-Tailed Confidence Level

    Confidence Levels

    Hypothesis Testing: A Six-Step Approach



    75 minutes

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