lab08.pdf - lab091 CS 237 Lab Nine Displaying Multivariate Data Due date PDF file due Thursday November 15st 11:59PM(10 off if up to 24 hours late in

lab08.pdf - lab091 CS 237 Lab Nine Displaying Multivariate...

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6/25/2019 lab091 localhost:8889/nbconvert/html/Desktop/CS237/lab091.ipynb?download=false 1/32 CS 237 Lab Nine: Displaying Multivariate Data Due date: PDF file due Thursday November 15st @ 11:59PM (10% off if up to 24 hours late) in GradeScope 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: - blog.udacity.com/posts/2016/10/latex-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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6/25/2019 lab091 localhost:8889/nbconvert/html/Desktop/CS237/lab091.ipynb?download=false 2/32 In [3]: # 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) # 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 :
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6/25/2019 lab091 localhost:8889/nbconvert/html/Desktop/CS237/lab091.ipynb?download=false 3/32 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
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  • Summer '19
  • Normal Distribution, Probability theory, probability density function, Cumulative distribution function, matplotlib

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