Exercise

# Cumulative distribution function

Understanding the logistic distribution is key to understanding logistic regression. Like the normal (Gaussian) distribution, it is a probability distribution of a single continuous variable. Here you'll visualize the *cumulative distribution function* (CDF) for the logistic distribution. That is, if you have a logistically distributed variable, `x`

, and a possible value, `xval`

, take `x`

could take, then the CDF gives the probability that `x`

is less than `xval`

.

The logistic distribution's CDF is calculated with the logistic function (hence the name). The plot of this has an S-shape, known as a *sigmoid curve*. An important property of this function is that it takes an input that can be any number from minus infinity to infinity, and returns a value between zero and one.

`ggplot2`

is loaded.

Instructions 1/2

**undefined XP**

Create a tibble containing three columns.

`x`

values as a sequence from minus ten to ten in steps of`0.1`

.`logistic_x`

made from`x`

transformed with the logistic distribution CDF.`logistic_x_man`

made from`x`

transformed with a logistic function calculated from the equation \(cdf(x) = \frac{1}{(1 + exp(-x))}\).- Check that both logistic transformations (
`logistic_x`

and`logistic_x_man`

) have the same values with`all.equal()`

.