'''Write a function that takes a list of numbers as input and returns

the mean of that input list.

In: List of integers

Out: The mean as an integer or float

Ex: find_mean([1,4,3,6,3,7,6,5,8,12])

>>> 5.5'''

# Two ways

np_mean = np.mean(np.array(data_lst))

py_mean = sum(data_lst) / len(data_lst)

'''Write a function that takes a list of numbers as input and returns

the median of that input list. Account for both even and odd length lists.

In: List of integers

Out: The median as an integer or float

Ex: find_median([1,4,3,6,3,7,6,5,8,12,9])

>>> 6'''

# With NumPy

np_med = np.median(np.array(data_lst))

# Without NumPy

sort_lst = sorted(data_lst)

if len(sort_lst) % 2 == 0:

mid1 = sort_lst[:len(sort_lst)//2][-1]

mid2 = sort_lst[len(sort_lst)//2:][0]

median = (mid1 + mid2) / 2

else:

median = sort_lst[len(sort_lst)//2]

'''Write a function that takes a list of numbers as input and returns

the mode of that input list. Assume there is only one mode.

In: List of integers

Out: The mode as an integer or float

Ex: find_mode([1,4,3,6,3,7,5,8,12,11])

>>> 3'''

# With ScipyStats

stats_mode = stats.mode(np.array(data_lst))[0][0]

# The hard way

counts_dict = {}

for each in data_lst:

if each in counts_dict.keys():

counts_dict[each] += 1

else:

counts_dict[each] = 1

py_mode = max(counts_dict, key=counts_dict.get)

'''Write a function that takes a list of numbers as input and returns

the variance of that input list. Notice the population=True argument:

write your code so that it calculates population variance if that argument

is True, and sample variance if it is False.

In: List of integers

Out: The variance as an integer or float

Ex: find_variance([1,4,3,6,3,7,5,8,12,11,0,34])

>>>74.4722222222'''

# With NumPy (this defaults to population variance)

np_var = np.var(np.array(data_lst))

# The hard way

mn = find_mean(data_lst)

dist = []

for each in data_lst:

dist.append(each - mn)

squares = []

for each in dist:

squares.append(each**2)

sums = sum(squares)

if population:

v = sums / len(data_lst)

else:

v = sums / len(data_lst) - 1

'''Write a function that takes a list of numbers as input and returns

the standard deviation of that input list. Use your variance function.

In: List of integers

Out: The standard deviation as an integer or float

Ex: find_stand_dev([1,4,3,6,3,7,5,8,12,11,0,34])

>>>8.629728977333079'''

# Two ways

np_std = np.sqrt(find_variance(data_lst))

py_std = find_variance(data_lst)**(1/2)

# Alicia, np and regular are a few digits off from each other

# in the tens of thousands decimal place, maybe we should add round for

# any in which the students might use either np or regular?

'''Given the probability of success, p and the possible outcomes, k

(1 or 0), and the number of trials, n (1), calculate the PMF, the E(X), and the Var(X) for

a binomial distribution.

In: p: probability of success, k: possible outcomes, n: num trials; all ints or floats

Out: PMF, E(X), Var(X), all integers or floats

Ex: bernoulli_pmf(0.4, 1, 1)

>>>0.4, 0.4, 0.24'''

p_s = p

p_f = (1-p)

ex = p

varx = p_s * p_f

pmf = (p_s**k) * (p_f**(n-k))

'''Given the probability of success, the total number of trials, and

the number of successful trials, calculate the PMF, E(X) and

Var(X) for the binomial distribution.

In: p: probability of success, k: possible outcomes; both ints or floats

Out: PMF, E(X), Var(X), all ints or floats.

Ex: binomial_pmf(0.6, 300, 24)

>>>8.207452839437304e+58, 13.600000000000001, 8.16'''

combs = (f(n)) / ((f(k))*(f(n-k)))

bern_pmf = bernoulli_pmf(p, n, k)[0]

pmf = combs * bern_pmf

ex = n*p

var = (n*p)*(1-p)

'''Given the rate, and k, the number of successes, write a function that

calculates the PMF, E(X) and Var(X) of the Poisson distribution.

In: The rate, k: number of successes; both ints or floats

Out: PMF, E(X), Var(X); all ints or floats

Ex: poisson_pmf(5, 0)

>>>0.006737946999085469, 5, 5'''

e = math.e

numer = (rate**k) * (e**-rate)

denom = f(k)

pmf = numer / denom

ex = rate

varx = rate