ENED $1120-S_1$

$324$

Homework $1\mathrm{.}2$: Python List and Functions

Note: Below are instructions for Tasks $1$ & $2$ of this homework. Please be sure to follow these specific instructions related to list formation and utilization of functions. The grading rubric is based on these specific instructions. Your Python script might be correct, but you can still lose points for not following the instructions.

Task $1($of $2)$: Frequency Distribution Function

In statistics, a frequency distribution of a dataset is an organized tabulation $($can also be graphical$)$ representation of the number of times the data is in each category $($also called bins$)$ on the scale of measurement. It allows the analyst to have a glance at the entire data conveniently. One way to estimate the number of bins based on sample size, $n$ is using the following equation:

Number $of$ bins $=1+$ceil$(lo{g}_2(n))$

where $lo{g}_2$ is $log$ base $2($search Google for help on how to do $log$ of $2$ in Python$).$ As the sample size increases so does the number of bins. The ceiling function $($ceil$)$ ensures that the result of the logarithm is an integer. Then the width of each bin is estimated as

Bin Width $=($ Max $-$ Min $)($ Number $of$ bins $)$

where Max and Min are respectively, the maximum and the minimum values.

Consider the following iterative process used to generate a dataset $x$

$x(i+1)=Y(i)$

with

$Y(i+1)=-b**x(i)+a**Y(i)-(Y(i){)}^{{?}^{{?}^{?}}}3$

Your task consists of creating a Python function called HW$2$p$1\_$Task$1\_$UCusername that works as follows