Question

Based on the number of voids, a ferrite slab is classied as either high, medium, or low. Historically, 5% of the slabs are classied as high, 90% as medium, and 5% as low. A sample of 20 slabs is selected for testing. Let X; Y; and Z denote the number of slabs that are independently classied as high, medium, and low, respectively

a. What is the joint probability distribution of X; Y; and Z and what are it's parameteres (n,p1...)?

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. Calculate 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 I Y = 17)

j. P(X = 2 I Y = 17)

k. E(X I Y = 17)

Answer 1