Answer:
Step-by-step explanation:
Given that:
A small-business Web site contains 100 pages and 60%, 30%, and 10% of the pages contain low, moderate, and high graphic content, respectively.
. A sample of four pages is selected without replacement,
Let X and Y denote the number of pages with moderate and high graphics output in the sample
We are meant to determine
a) from the given data in the question;
However; the probability mass function can be expressed via the relation:
We can now have a table shown as :
0 1 2 3 4 Total
0 0.1244 0.0873 0.02031 0.0018 0.0001 0.234
1 0.2618 0.13542 0.02066 0.00092 0 0.419
2 0.1964 0.0666 0.00499 0 0 0.268
3 0.0621 0.01035 0 0 0 0.073
4 0.0069 0 0 0 0 0.007
Total 0.6516 0.2996 0.0460 0.0028 0.0001 1
b)
The marginal distribution definition of
From the table above ; the corresponding values of are :
X 0 1 2 3 4
0.234 0.419 0.268 0.073 0.007
( since represent the vertical column)
c) E(X)
By using the expression
we have:
E(X) =
E(X) = 0 + 0.419 + 0.536 + 0.218 + 0.028
E(X) = 1.202
d) fyß(y)
Using the thesis of conditional Probability; we have :
The conditional probability for the mass function is then:
where;
values of for every y ∈ (0,1,2,3,4)
Therefore; the mass function is:
e) E(Y | X = 3)
By using the expression
we have:
⇒
= 0.143
The value of E(Y | X = 3) = 0.143
g) Are X and Y independent?
To Check if X and Y independent; Let assume if ; then we can say that X and Y are independent.
From the above previous table :
= 0.1244 + 0.087268+0.02031+ 0.001836 + 0.0001
= 0.234
We conclude that ; As such X and Y are said to be non - independent.