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[.pdf]
(a more fun alternative from
the 2004/5 MBA guide))
Doctoral Program in Statistics:
If you are interested in our Ph.D. program, please, visit
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Once you decide to apply, start your application
at this website.
source("http://stat.wharton.upenn.edu/~buja/STAT-101/src-probability.R")Here are things that can be done:
X <- make.RV(1:6, rep("1/6",6)) # Create a fair die (class: "RV") Y <- make.RV(1:6, c(0.1,0.1,0.1,0.1,0.2,0.4)) # Create a loaded die ( '' ) P(X>3); P(Y>3) # Probabilities of events E(X); E(Y) # Expected values V(X); V(Y) # Variances SD(X); SD(Y) # Standard deviations par(mfrow=c(2,1)); plot(X); plot(Y) # Plot as pin graphs S <- SofI(X,Y); par(mfrow=c(1,1)); plot(S) # Sum of two independent RVs S10 <- SofIID(X,10); plot(S10) # Sum of 10 iid copies of X (works for many more => CLT) qqnorm(S10) # Normal quantile plot for RVs to check the CLT effect X.sim <- rsim(1000, X) # Simulate from X (class: "RVsim") plot(X.sim) # Plot simulated data as pin graph probs(X); props(X.sim) # Compare probabilites and simulated proportions E(X); mean(X.sim) # Compare expected value and mean SD(X); sd(X.sim) # Compare theoretical and observed std.dev. X2 <- X^2; X2; plot(X2) # univariate analytical transformation Yexp <- exp(Y); Yexp; plot(Yexp) # '' Yfair <- Y - E(Y); Yfair # Centering a RV: creates a fair game from a loaded die Z <- (X - E(X))/SD(X); Z; plot(Z) # z-scoring/standardizing a random variable Ybern <- con(ifelse(Y>3,1,0)) # Create a Bernoulli variable; 'con()' contracts values/probsCheck the header of the source file for more explanations and examples.
source("http://stat.wharton.upenn.edu/~buja/PAPERS/src-conspiracy-animation.R") source("http://stat.wharton.upenn.edu/~buja/PAPERS/src-conspiracy-animation2.R")The source code is in two files: the simple version showing nonlinearity only, and the augmented version showing nonlinearity and linearity.
source("http://stat.wharton.upenn.edu/~buja/association-navigator.R")