Computer Assignment 2 - Stockholms universitet

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ans =0.2001for N = 10, p = 0.3 and k = 4.The corresponding value of the cumulative distribution function( )k∑ NΦ(k, N, p) = p i (1 − p) N−ii=0ican just as easily be obtained using binocdf(k,N,p) as>> binocdf(4,10,0.3)ans =0.8497If you do not have access to the statistics toolbox, you can still calculate the cumulativedistribution function as>> for i=0:4p(i+1)=nchoosek(10,i)*power(0.3,i)*power(1-0.3,10-i);end>> sum(p)ans =0.8497where the function nchoosek yields the binomial coefficient ( )10i . Since it is often necessaryto make these calculations several times when analysing properties of options, you cancreate the file binocdf.m, placed in the directory where you work with Matlab, with thecontentfunction y=binocdf(k,N,p)f(1)=power(1-p,N);for i=1:Nf(i+1)=f(i)*(N-i+1)/i*p/(1-p);endfor i=1:length(k)y(i)=cumsum(f(k(i)+1));end(This is similar to the implementation in Matlab, where you can use a vector x as anargument.)2
1.2 The Normal DistributionThe probability density function for the normal distributionf(x) = √ 1 e − (x−µ)22σ 22πσcan be determined in Matlab through the function normpdf(x,m,s) as>> normpdf(1.5,2,0.7)ans =0.4416for x = 1.5, µ = 2 and σ = 0.7. Note that the third argument is the standrad deviationand not the variance.The cumulative distribution functionF (x) =∫ x−∞can be calculated using normcdf(x,m,s) as>> normcdf(1.5,2,0.7)ans =0.23751√ e − (y−µ)22σ 2 dy2πσIf you are interested in the corresponding functions for the standard normal distribution,it is not necessary to state the last two arguments. Instead you can write>> normpdf(1.5)ans =0.1295>> normcdf(1.5)ans =0.93323
Page 1: STOCKHOLM UNIVERSITY September 27,
Page 5 and 6: Note that τ = 1/250 in this case s

Computer Assignment 2 - Stockholms universitet

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