Answer:
A. (Table Attached)
B. (See Step 3)
C. 0.06 (See Step 4)
D. NOT independent (See Step 5)
Step-by-step explanation:
<h3 /><h3>STEP 1:</h3>
Name the probabilities:
p₁ = 0.02,   p₂ = 0.07,   p₃ = 0.91
q₁ = 1-p₁ = 0.98 ,   q₂ = 1-p₂ = 0.93 ,   q₃ = 0.09
Let X and Y be the number of bits with high and moderate distortion out of three.
<h3>STEP 2:</h3>
A.
The function will follow multinomial distribution:

Substitute the values and make a table.
TABLE IN ATTACHMENT
<h3>
STEP 3:</h3>
B.
We calculate marginal distribution by:
 <em>∑</em>
 <em>∑</em> 
 can be found by adding all the probabilities in each row for different value of X
 can be found by adding all the probabilities in each row for different value of X
For X=0 , ∑P = 0.94157441
For X=1 , ∑P = 0.057624
For X=2 , ∑P = 0.001176
For X=3 , ∑P =0.000008
<h3>
STEP 4:</h3><h3>
C.</h3>
The mathematic expectation E is the sum of product of each possibility with its probabiity.
 <em>∑ </em>
<em>∑ </em>
Find E(X):


<h3>
STEP 5:</h3>
Condition probability states:

It can also be written as:

Where  = 0.057624
 = 0.057624
Calculate the quotient:
 = 0 ,
 = 0 ,   = 0.862245
 = 0.862245
 = 1 ,
 = 1 ,   = 0.132653
 = 0.132653
 = 2 ,
 = 2 ,   = 0.000510
 = 0.000510
 = 3 ,
 = 3 ,   = 0
 = 0
Find the dependency:

We found that 
 = 0.862245
 = 0.862245
Calculate  from summing the column from the table
 from summing the column from the table

Which are not equal.
Conclusion:
X and Y are NOT Independent