09. A Gaussian Class

Gaussian Class

Gaussian Class

Resources for Review

The example in the next part of the lesson assumes you are familiar with Gaussian and binomial distributions.

Here are a few formulas that might be helpful:

Gaussian Distribution Formulas

probability density function
f(x \space | \space \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}}e^-\frac{(x-\mu)^2}{2\sigma^2}
\begin{aligned} \\ \text{where:} \\ \mu& \space \text{is the mean} \\ \sigma& \space \text{ is the standard deviation} \\ \sigma&^2 \space \text{is the variance} \end{aligned}

Binomial Distribution Formulas

mean
\mu = n * p

In other words, a fair coin has a probability of a positive outcome (heads) p = 0.5. If you flip a coin 20 times, the mean would be 20 * 0.5 = 10; you'd expect to get 10 heads.

variance
\sigma^2 = n * p * (1 - p)

Continuing with the coin example, n would be the number of coin tosses and p would be the probability of getting heads.

standard deviation
\sigma = \sqrt{n * p * (1 - p)}

or in other words, the standard deviation is the square root of the variance.

probability density function
f(k, n, p) = \frac{n\footnotesize{!}}{k!(n - k)!}p^k(1-p)^{(n-k)}

Further Resources

If you would like to review the Gaussian (normal) distribution and binomial distribution, here are a few resources:

This free Udacity course, Intro to Statistics , has a lesson on Gaussian distributions as well as the Binomial distribution.

This free course, Intro to Descriptive Statistics , also has a Gaussian distributions lesson.

Here are the wikipedia articles:

Quizzes

Here are a few quizzes to help you determine how well you understand the Gaussian and binomial distributions. Even if you can't remember how to answer these types of questions, feel free to move on to the next part of the lesson; however, the material assumes you know what these distributions are and that you know the basics of how to work with them.

Probability

Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs exactly 185 pounds?

SOLUTION: 0

Follow up question

Like in the previous question, assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs somewhere between 120 and 155 pounds?

SOLUTION: 0.19

Binomial Distribution

Now consider a Binomial distribution. Assume that 15% of the population is allergic to cats. If you randomly select 60 people for a medical trial, what is the probability that 7 of those people are allergic to cats?

SOLUTION: 0.12

Next Concept