Find the area of a parallelogram with vertices at P(–8, –3), Q (–7, 3), R(–9, 3), and S(–10,

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

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

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.

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

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

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):

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

$E(X)=0.06$

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

7 0

3 years ago

A conjecture and the paragraph proof used to prove the conjecture are shown.

kotegsom [21]

1. Linear Pair Postulate
2. MAngle 3
3.Angle 3
4.Angle Congruence Postulate

Hope this helps!
-Soul

6 0

3 years ago

Read 2 more answers

Subtraction is a commutative operation. When writing an expression for the difference of two numbers, it does not matter what or

Mice21 [21]

A.True they can be switched around

7 0

2 years ago

Read 2 more answers

313 people were surveyed in total. 183 of the people surveyed are from East Harlem and 130 people are from the Upper East Side.

borishaifa [10]

1. The percentage of people surveyed in East Harlem is 58.5%

2. The percentage of people surveyed in Upper East Side is 41.5%

From the question given above, the following data were obtained:

People surveyed in East Harlem = 183

People surveyed in Upper East Side = 130

Total people surveyed = 313

1. Determination of the percentage of people surveyed in East Harlem.

People surveyed in East Harlem = 183

Total people surveyed = 313

Percentage of East Harlem =?

Percentage of East Harlem = (people surveyed in East Harlem / Total) × 100

Percentage of East Harlem = (183/313) × 100

Percentage of East Harlem = 58.5%

2. Determination of the percentage of people surveyed in Upper East Side.

Percentage of East Harlem = 58.5%

Total percentage = 100%

Percentage of Upper East Side =?

Percentage of Upper East Side = (Total percentage) – (Percentage of East Harlem)

Percentage of Upper East Side = 100 – 58.5

Percentage of Upper East Side = 41.5%

Learn more about percentage:

brainly.com/question/14899205

7 0

2 years ago

Which is a factor of each term of the polynomial? (72−12) CLEAR CHECK 7 2 7

Inessa [10]

Answer:

12

Is the greatest factor

Step-by-step explanation:

All factors include

2,3,4,6,12

Thats it

3 0

2 years ago

Find the area of a parallelogram with vertices at P(–8, –3), Q (–7, 3), R(–9, 3), and S(–10, –3).