Descriptive Statistics

calculate basic descriptive statistics for a data set

{25, 35, 10, 17, 29, 14, 21, 31}

compute a statistical quantity

mean {21.3, 38.4, 12.7, 41.6}

kurtosis {21.3, 38.4, 12.7, 41.6}

Statistical Inference

find sample size needed to estimate a binomial parameter

sample size for binomial parameter

compute a confidence interval for a population mean

t-interval xbar=4.15, s=0.32, n=100

apply a test for a population mean

z-test for population mean

Regression Analysis

fit a line to two-dimensional data

linear fit {1.3, 2.2},{2.1, 5.8},{3.7, 10.2},{4.2, 11.8}

fit a polynomial to given data

cubic fit 20.9,23.2,26.2,26.4,16.3,-12.2,-60.6,-128.9

fit an exponential model to given data

exponential fit 0.783,0.552,0.383,0.245,0.165,0.097

Statistical Distributions

compute properties of a probability distribution

Poisson distribution

specify parameters for a distribution

normal distribution, mean=0, sd=2

compute a particular property

standard deviation of Student t, 17 degrees of freedom

Random Variables

compute the expected value of a random variable

X~Poisson(7.3), EV[3X^4-7]

compute the probability of an event

P[-1.2<X<2.3] for X~student t with 12 dof

Probability

compute the probability of a union of events

probability of the union of three events

compute coin toss probabilities

32 coin tosses

compute odds for a poker hand

poker full house

analyze a wager

8:5 odds, bet 97 euros

compute the probabilities of shared birthdays for a group of people

birthday paradox 50 people