---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- Multinomial distribution # An automatic oven produces on average 1 biscuit burnt every 8; biscuits are then # automatically mixed and packaged in packs of 6. What is the distribution law of the # random variable N = "n. of burnt cookies in a pack"? # It is a discrete probability distribution. N = 6; p = 1/8; x = 0:N; y = dbinom(x, N, p) # x[1]=0, ..., x[N+1]=N, y[1]=... Piano(0,N, 0,max(y)); POINT(x,y, "blue") # If the burnt cookies are 3: a=2; b=dbinom(a,N,p); b; fraction(b); POINT(a,b,"red") # graph on the left: # Using multinomial instead of binomial: N = 6; p = 1/8; x = 0:N for(i in 0:N) y[i+1] = dmultinom(c(i,N-i), prob=c(p,1-p) ) Piano(0,N, 0,max(y)); POINT(x,y, "blue") a=2; b=dmultinom(c(a,N-a),prob=c(p,1-p)); b; fraction(b); POINT(a,b,"green") # graph on the right # # See here and here for specific examples.