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PH24010 MathCAD Statistics, Random Numbers & Histograms Distribution Functions • dnorm(x, , ) – Normal distribution 0.4 dnorm x 0.2 • pnorm(x, , ) – Cumulative Normal distribution – Equal to x dnorm x d x 0 4 2 0 x 2 4 4 2 0 x 2 4 1 dnorm x pnorm x 0.5 0 Other distributions • Poisson – dpois(r,l) ppois(r,l) – r events in distribution with mean l • Binomial – dbinom(k,n,p) pbinom(k,n,p) – k success in n trials, probability p • Exponential – dexp(x,r) – Exponential distribution, decay rate r Histograms • histogram(Intvls, Data) • Returns Matrix • Results<0> – Midpoints of intervals • Results<1> 30 20 Counts 10 – Count per bin 0 3 2 1 0 Bins 1 2 3 The Intervals vector • Gives endpoints of intervals • n elements in vector • n-1 midpoints • Watch for Fencepost error • Off-by-one-error – Obi-One-’kin-Error 0 1 Intervals 2 3 4 0.5 1.5 midpoints 2.5 3.5 Generating the Intervals Vector • Program • Local Variables • for loop • Use programming toolbar • Test program IntervalVectoramin ( amax Np ) a amax amin Np for i 0 Np Resulti amin a i Result 0 2 4 IntervalVector0 ( 10 5) 6 8 10 Coins, Dice & other random things • rnd(x) random number in range 0 to x • manipulate to get desire result • rnd(1)>0.5 will give – 0 for 50% and – 1 for 50% – True=1, false =0 • int(rnd(6)) gives number 0 to 5 Other Random Distributions Return vector of m numbers • • • • rnd(m,a,b) uniform distribution rnorm(m, , ) normal distribution rpois(m,l) Poisson distribution rexp(m,r) exponential distribution • ++ others • see f(x) & help Pseudo-Randomness & seed • • • • • Numbers generated in sequence Same sequence every time worksheet run SEED variable sets start point in sequence Integer from 1 to 2147483647 Change seed with – Tools|Worksheet Options|Built-in variables – Seed(x) • Seed(trunc(time(0)))