Mathematics UpperSecondary 4  Distributions and Integration
Increase your understanding of distribution and integration in mathematics with this free online course.
Description
This course begins by introducing you to random variables. You will learn that a random variable is a variable whose value is a numerical outcome of some random experiment. You will study the discrete probability distribution, the mean and variance of a discrete random variable, and the standard deviation as a measure of spread. You will also look into normal distribution and its calculation of probabilities, binomial distribution and the binomial probability function, and hypergeometric distribution and the formula for calculating probabilities.
You will then look into the rules of integration. You will learn that antidifferentiation is the reverse of differentiation and you can use this process to find a function from a derivative. You will also study integration applications including areas, integral calculus, and definite integrals. You will study how to approximate an area and evaluate a definite integral where you will learn that areas above the axis are positive and areas below are negative.
This course will help you understand mathematical calculations in an easy, stepbystep process. Upon the completion of this course, you will understand the meaning of random variables and be able to calculate the discrete probability distribution of a set of random variables, continuous random variables, and normal distribution. You will gain a good knowledge of binomial probability function, distribution, hypergeometric distribution, rules of integration and integration applications so make sure to check out this course and enhance your math skills today!
Modules
Binomial distribution

Binomial probability function and distribution

The number of successes in a given number of trials

The effect of changing the parameter p

The effect of changing the parameter n

The mean and variance of a binomial random variable
Discrete random variables

Random variables

Discrete probability distribution

The mean and variance of a discrete random variable

Standard deviation as a measure of spread
Hypergeometric distribution

Sampling without replacement

The mean of a hypergeometric random variable

The variance of a hypergeometric random variable

The mean and variance of a hypergeometric random variable example

The mean and variance of a hypergeometric random variable example 2

The formula for calculating probabilities

Calculating probabilities

Relationship between hypergeometric and binomial distributions
Integration applications
Glossary
Normal distribution

The normal curve

Continuous random variables and the normal distribution

Calculation of probabilities for a normal distribution

Approximating the binomial distribution with normal distribution
Rules of integration

Antidifferentiation

Antiderivatives of basic functions

Finding specific functions based on given information

Indefinite integral

Using related derivatives to find an integral
Assessment
Learning Outcomes
On completion of this course you will understand the meaning of random variables and be able to calculate the dicrete probability distribution of a set of random variables, continuous random variables and normal distribution.
You will gain a good knowledge of binomial probability function, distribution, hypergeometric distribution, rules of integration and intergration applications.
This course will help you to understand these calculations in an easy, stepbystep process.
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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