Your task consists of creating a Python function called HW

$2$

p

$1$

$\_$

Task

$1$

$\_$

UCusername that works

as follows

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$$

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To call your function, the user will type in the Python Shell, the name of the function

$$

HW

$2$

p

$1$

$\_$

Task

$1$

$\_$

UCusername

$$

$$

$$

and the arguments variables a

$,$

$$

$$

b

$,$

$$

$$

and n

$($

sample size

$)$

$.$

UCusername is what you use to login to CANVAS.

$$

$$

$$

Your function will then

o Set the initial value of X to

$0$

$.$

$1$

$$

$$

and the initial value of Y to

$0$

$.$

$2$

$.$

o Compute and store the successive values of X in a list using Equations

$($

$3$

$)$

$$

$$

and

$($

$4$

$)$

$.$

$$

$$

This

should be done using a repetition structure

$($

for or while loop

$)$

$$

$$

and Python

$$

s append

built

$-$

in function for adding on to lists.

o Compute the number of bins based on the sample size and using the Equation

$($

$1$

$)$

o Compute the width of each bin using Equation

$($

$2$

$)$

$$o Store the frequency distribution in Python as a list, i

$.$

e

$.$

$,$

$$the number of elements of X in

each bin. Complete this step using repetition structures

$($

for or while loop

$)$

$$and Python

$$

s

append built

$-$

in function. The goal is to generate a repetition structure that will adjust

based on the number of bins, see the third hint below for more guidance.

o Print the list with the frequency distribution to Python Shell. The equations are Number of bins $=1+$ ceil$($log$2($n$))(1)$

where log$2$ 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$)(2)$

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$)(3)$

with

y $($i$+1)=-$b $*$ x$($i$)+$ a $*$ Y$($i$)-($Y$($i$))^3(4)$