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>
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>
Find E(X):
<h3>STEP 5:</h3>
Condition probability states:
It can also be written as:
Where = 0.057624
Calculate the quotient:
= 0 ,
= 0.862245
= 1 ,
= 0.132653
= 2 ,
= 0.000510
= 3 ,
= 0
Find the dependency:
We found that
= 0.862245
Calculate from summing the column from the table
Which are not equal.
Conclusion:
X and Y are NOT Independent
