Based on the number of voids, a ferrite slab is classified as either high, medium, or low. Historically, 5% of the slabs are classified as high, 85% as medium, and 10% as low. A sample of 20 slabs is selected for testing. Let X, Y , and Z denote the number of slabs that are independently classified as high, medium, and low, respectively. 

(a) What are the name and the values of the parameters of the joint probability distribution of X, Y , and Z?

(b) What is the range of the joint probability distribution of X, Y , and Z?

(c) What are the name and the values of the parameters of the marginal probability distribution of X?

(d) Determine E(X) and V (X).

Determine the following:

(e) P(X = 1, Y = 17, Z = 3) 

(f) P(X ≤ 1, Y = 17, Z = 3)

(g) P(X ≤ 1) 

(h) E(Y )

(i) P(X = 2, Z = 3 |Y = 17) (j) P(X = 2 |Y = 17)

(k) E(X |Y = 17)