Stat 11 – Honors Statistics with Mathematica Mathematica does calculations with exact arithmetic, so calculations can be done to any degree of accuracy. Several calculations in Chapter 4 were done using factorials and binomial coefficients, so we begin with these. 10! Binomial coefficients can be found easily. Binomial[n, s] represents the usual symbol ⎟⎟⎠⎞⎜⎜⎝⎛snso for example ⎟⎟⎠⎞⎜⎜⎝⎛310 is Binomial[10, 3] So here is part of one of test 2’s problems Binomial[3, 2](.6)^2*(.4) The whole thing, this is a print of the entire table or probability distribution of random variable x Table[{x, Binomial[3, x]((.6)^x)((.4)^(3-x))},{x,0,3}] The Normal Distribution is specified by the Mathematica function NormalDistribution[µ, σ] Suppose you need to calculate the probability that the normal random variable X exceeded 1150 for a N[1000,200] distribution. This can be done by Mathematica in several ways: 1 - CDF[NormalDistribution[1000, 200], 1150] // N Integrate[PDF[NormalDistribution[1000, 200], x],{x, 1150, Infinity}] // N The mathematical expression for the normal probability distribution function could also be used with the same result. There is no need for the z transformation when Mathematica is available, but calculations can be made using it. Here are the calculations for the “68, 95, 99” Rule to 10 decimal places. N[CDF[NormalDistribution[0, 1], 1] - CDF[NormalDistribution[0, 1], -1], 10] N[CDF[NormalDistribution[0, 1], 2] - CDF[NormalDistribution[0, 1], -2], 10] N[CDF[NormalDistribution[0, 1], 3] - CDF[NormalDistribution[0, 1], -3], 10] To find the Z score Quantile[NormalDistribution[0, 1], 0.975] or for an arbitrary normal distribution, like IQ Quantile[NormalDistribution[100, 15], 0.975] randomDie:=Random[Integer,{1,6}] A random walk is a random process consisting of a sequence of discrete steps of fixed length. Random walk theory gained popularity in 1973 when Burton Malkiel wrote A Random Walk Down Wall Street, a book that is now regarded as an investment classic. Random walk is a stock market theory that states that the past movement or direction of the price of a stock or overall market cannot be used to predict its future movement. OriginallyStat 11 – Honors Statistics with Mathematica examined by Maurice Kendall in 1953, the theory states that stock price fluctuations are independent of each other and have the same probability distribution, but, over a period of time, prices maintain an upward trend. In short, random walk says that stocks take a random and unpredictable path. The chance of a stock's future price going up is the same as it going down. A follower of random walk believes it is impossible to outperform the market without assuming additional risk. In his book, Malkiel preaches that both technical analysis and fundamental analysis are largely a waste of time and are still unproven in outperforming the