1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PilotLPTM [1.2K]
3 years ago
6

In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

0.91, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let and denote the number of bits with high and moderate distortion out of the three, respectively. Determine the following:
A. fxy(x,y).
B. fx(x).
C. E(X).
D. Are X and Y independent?

Mathematics
1 answer:
Leviafan [203]3 years ago
7 0

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:

f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})

Substitute the values and make a table.

TABLE IN ATTACHMENT

<h3>STEP 3:</h3>

B.

We calculate marginal distribution by:

P (X=x)= <em>∑</em> P(X=x,Y=y)

fx(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.

E(X)=<em>∑ </em>xP(X=x)

Find E(X):

E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)

E(X)=0.06

<h3>STEP 5:</h3>

Condition probability states:

P(A|B)=\frac{P(A,B)}{P(B)}

It can also be written as:

f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}

Where f_x(1)\\ = 0.057624

Calculate the quotient:

Y|_{x=1} = 0 ,  f_{Y|_X=1 = 0.862245

Y|_{x=1} = 1 ,  f_{Y|_X=1 = 0.132653

Y|_{x=1} = 2 ,  f_{Y|_X=1 = 0.000510

Y|_{x=1} = 3 ,  f_{Y|_X=1 = 0

Find the dependency:

f_{XY}(y)=f_X(x)f_Y(y)

We found that

f_{Y|_X=1 = 0.862245

Calculate f_Y(1) from summing the column from the table

f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141

Which are not equal.

Conclusion:

X and Y are NOT Independent

You might be interested in
The equation with one change and no solutions: 8x + 6 =
Lisa [10]
The answer is 2 ........
6 0
3 years ago
PLEASE ANSWER THIS QUESTION ASAP
Brilliant_brown [7]

Answer:

its Aor the first option because it has repeated x values making it not a function.

5 0
3 years ago
What are the different communication models?<br><br><br>​
Illusion [34]

Answer:

The three most well known models for communication are Linear, Interactional, and Transactional. As West & Turner (2007) explain, each model sheds light on the development of communication, but emphasizes different parts of the communication process.

Step-by-step explanation:

mark me as the brainliest

8 0
2 years ago
Read 2 more answers
9(y-4) -3y = 2(3y-2 need solved as fast as possible
Vlad [161]

Step-by-step explanation:

did you give us all the information ? the equating looks cut off.

so, from what I can see we have

9(y-4) - 3y = 2(3y-2)

let's try :

9y - 36 - 3y = 6y - 4

0 = 32

so, no, this can't be it. this does not have a solution. you must have cut off some additional information.

7 0
3 years ago
686.924 rounded to the nearest ten
bixtya [17]
690 because 86 is rounded up to 90
8 0
3 years ago
Read 2 more answers
Other questions:
  • The table shows the amount of red paint that can be added to different amounts of white paint while making a custom paint color:
    7·1 answer
  • Ava has 34 candy bars. If
    11·1 answer
  • Help 10 minutes to turn in
    15·1 answer
  • Are the ratios equivalent? 2/3 and 8/12 Explain.
    6·2 answers
  • Need help asap pleas and thank you .
    9·1 answer
  • Convert 49° Celsius to degrees Fahrenheit using the following formula: F = {C+32 O A. 506.5°F OB. 196.2°F C. 94.6°F OD. 2237°F O
    15·1 answer
  • Can someone help me do this darn work plz
    15·2 answers
  • Please help solve this I have been raking my brain for hours​
    6·1 answer
  • Divide: (12x4 + 9x3 – 10x2) ÷ 3x3
    5·2 answers
  • Describe how to write 8,231,000,000 in scientific notation.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!