(X_{1},...,X_{r})~Multi(n,r,p_{1},...,p_{n})
The above is the multinomial distribution
a). if there are 100 apples and 4 baskets, 1 basket must have 15 apple, 2nd basket must have 35 apples, basket 3 must have 20 apples, and basket 4 must have 30 apples how many ways can you divid the apples in the 4 baskets
b)\binom{n}{k_{1},k_{2},...,k_{r}}=\frac{n!}{k_{1}!*k_{2}!*...*k_{r}!}is the multinomial coefficient.
rewrite part a in terms of the multinomial coefficient.
c) Find the joint p.m.f of the Multinomial distribution,p_{X_{1}},...,_{X_{r}}(k_{1},...,k_{r})
d)show Multi(n, 2, p1, p2) is equal to the binomial distribution
e)what's the marginal distribution of X1
f).find an expression forCov(X_{i},X_{j}), for i,j=1,...,r