What is the question want? Do i need to do a Binomial Law for the j and then plot the CDF?

Question

Given an experiment that follows Binomial Law, b(k, 10; 0.2). Define the RV X by 𝑋(𝑘) = { 0; 0 ≤ 𝑘 ≤ 2 1; 2 < 𝑘 ≤ 5 2; 5 < 𝑘 ≤ 7 3; 7 < 𝑘 ≤ 10 Compute the probabilities P[X = j] for j = 0, 1, 2, and 3. Plot the CDF for all x.

Answer 1

It seems the question is saying that

P(X=0) = Bin(0,10, 0.2)+Bin(1,10, 0.2)+Bin(2,10, 0.2)

P(X=1) = Bin(3,10, 0.2)+Bin(4,10, 0.2)+Bin(5,10, 0.2)

P(X=2) = Bin(6,10, 0.2)+Bin(7,10, 0.2), and

P(X=3) = Bin(8,10, 0.2)+Bin(9,10, 0.2)+Bin(10,10, 0.2)