https://classroom.github.com/a/8OaR5UEl

**Due: 2020-02-21 by 11:59pm**

Come up with your own probability density function over the support \(S = \{1, 2, 3, 4 \}\). Name this vector

`f`

in R.Calculate the expected value of this distribution and store it into a variable. With vectorization, this should happen in one line (excluding printing).

Calculate the standard deviation of this distribution. With vectorization, this should happen in one more line from the above.

Generate some random data from this distribution, using the function

`sample()`

and its argument`prob`

.Estimate the population mean using only your sample. Is this a reasonable estimate of the population mean (expected value)?

Estimate the population standard deviation using only your sample. Is this a reasonable estiamte of the population standard deviation?

Come up with two vectors of 5 observations each that have the same mean, but different standard deviations. Explain why one has a larger standard deviation? What is it about the data that makes it have a larger standard deviation.

Come up with two vectors of 5 observations that have the same standard deviation, but different means. Explain why one has a larger mean? What is it about the data that makes it have a larger mean.