# EXAMPLE 4 (d) - MODULE 3

###########################################################

n = 20  # number of chips
k = 5   # number of drawn chips
y = seq(k,n,1);print(y)

r = length(y);print(r)

F = choose(y,k)/choose(n,k);print(F)

F = round(F,4);print(F)

f = rep(0,r);print(f)

f[1] = F[1]  #  This is the probability that Y=5
f[2:r] = F[2:r] -F[1:r-1] 

print(f)

cbind(y,f,F)

mu = sum(y*f); print(mu)  #  to calculate mu = E(Y)

mu2 = sum(y^2*f); print(mu2)  #  to calculate mu2 = E(Y^2)

s2 =mu2 - mu^2; print(s2)    #  to calculate Var(Y) = mu2 - mu^2

s =sqrt(s2); print(s)    #  to calculate SD(Y) = (mu2 - mu^2)^1/2


print(paste('mean = ',round(mu,3)),quote = FALSE)

print(paste('Variance = ',round(s2,3)),quote = FALSE)

print(paste('SD = ',round(s,3)),quote = FALSE)