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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.

OBJECTIVES

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

COURSE OUTLINE

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

PREREQUISITE KNOWLEDGE

Probability - View Now

ESTIMATED COMPLETED TIME

75 minutes

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