hw08A.solution.pdf - lab09.solution CS 237 Homework 8 A Displaying Multivariate Data General Instructions Please complete this notebook by ﬁlling in

# hw08A.solution.pdf - lab09.solution CS 237 Homework 8 A...

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6/22/2019 lab09.solution 127.0.0.1:8889/notebooks/lab09.solution.ipynb 1/25 CS 237 Homework 8 A: Displaying Multivariate Data General Instructions Please complete this notebook by filling in solutions where indicated. Be sure to "Run All" from the Cell menu before submitting. You may use ordinary ASCII text to write your solutions, or (preferably) Latex. A nice introduction to Latex in Jupyter notebooks may be found here: (- primer/) As with previous homeworks, just upload a PDF file of this notebook. Instructions for converting to PDF may be found on the class web page right under the link for homework 1.

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6/22/2019 lab09.solution 127.0.0.1:8889/notebooks/lab09.solution.ipynb 2/25 In [1]: # General useful imports import numpy as np from numpy import arange,linspace, mean, var, std, sin, cos from numpy.random import random, randint, uniform, choice, binomial, geometric, poisson import math from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt from matplotlib import cm import matplotlib.mlab as mlab from matplotlib.ticker import LinearLocator, FormatStrFormatter from collections import Counter #import pandas as pd % matplotlib inline # Basic Numpy statistical functions X = [1,2,3] # mean of a list mean(X) # might need to use np.mean, np.var, and np.std # population variance var(X) # sample variance ddof = delta degrees of freedom, df = len(X) - ddof var(X,ddof=1) # population standard deviation std(X) # sample standard deviation std(X,ddof=1) # Scipy statistical functions # Scipy Stats Library Functions, see: # from scipy.stats import norm,t,binom,geom,expon,poisson,uniform,bernoulli # Uniform over interval [0..1) # generate n random variates n=1000 uniform.rvs(size=n) # Bernoulli # generate n random variates p=0.5 bernoulli.rvs(p,size=n) # Binomial: X ~ B(n,p) # Example parameters k = 4 n = 10 p = 0.5 # Probability Mass Function: P(X = x) binom.pmf(k, n, p) # Cumulative Distribution Function: P(X <= x) binom.cdf(k, n, p)
6/22/2019 lab09.solution 127.0.0.1:8889/notebooks/lab09.solution.ipynb 3/25 # Generate n random variates binom.rvs(n, p, size=n) # Geometric Distribution X ~ G(p) # Probability Mass Function: P(X = k) geom.pmf(k,p) # Cumulative Distribution Function: P(X <= k) geom.cdf(k,p) # Generate n random variates geom.rvs(p,size=n) # my own version of the previous which only generates rvs up to # a limit -- this is not the same as the original distribution but # useful for displaying data in which you want to fix the size of the display def geom_rvs(p=0.5,size=1,limit=20): if size ==1: x = geom.rvs(p) while x > = limit: x = geom.rvs(p) return x else : lst = [0] * size for k in range(size): x = geom.rvs(p) while x > = limit: x = geom.rvs(p) lst[k] = x return lst # Poisson Distribution X ~ Poisson(lam) lam = 2 k=3 # P(X = k) poisson.pmf(k,lam) # P(X <= k) poisson.cdf(k,lam) # P(X > k) poisson.sf(k,lam) # Generate n random variates poisson.rvs(lam,size=n) # Exponential # Example parameters lam = 2 # rate parameter beta = 1 / lam # mean k = 2 # Probability density function expon.pdf(k,scale=beta) # Cumulative Distribution Function: P(X <= k) expon.cdf(k,scale=beta) # P(X > k) expon.sf(k,scale=beta)

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