The event of k successes in n tries regardless of the order

The event of k successes in n tries regardless of the order is the binomial law b(k,n; p). Let n = 10, p = 0.3. Define the random variable X by

X(k)=   1, for (0<= k <= 2)    2, for (2< k <=5)      3, for (5 < k <=8)     4, for (8 < k <=10)

Comput the probabilities P[X=j] for j = 1,...,4. Plot the CDF F_X(x)=P[X <= x] for all x.

Solution