Pleaaaseee helpppppp

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

2 years ago

if 7 < 5, then 5 < 3 state the inverse, contrapositive, and converse of each conditional statement. then indicate whether

RUDIKE [14]

The given conditional statement is : If 7<5, then 5<3.

Inverse: If 7≥5 then 5≥3 (The inverse is true)

Contrapositive: if 5≥3 then 7≥5 (The contrapositive is true)

Converse: if 5<3 then 7<5 (The converse is true)

From the properties of conditional statement we know that:

if p→q then

inverse is : $\backsim p \rightarrow \backsim q$

contrapositive: $\backsim q \rightarrow \backsim p$

Converse: $q \rightarrow p$

Let us elaborate on the above conditions. Let us take two statement p and q such that If p happens then q also happens.

The inverse of a conditional statement is given as "if not p then not q"the converse is given as "if q then p"The contrapositive of the statement states "if not q then not p"

The following statements can be used for converting the conditional statements to its inverse, converse or contrapositive.

To learn more about conditional statements:

brainly.com/question/7066208

#SPJ4

3 0

9 months ago

Umm whats y2 when y is -9 and whats z2 when z is 0.7 im not that smart so ill be asking alot

Dmitry_Shevchenko [17]

Answer:

Step-by-step explanation:

y = - 9

y^2 = (-9)^2 = 81

AND

z = 0.7

z^2 = (0.7)^2 = 0.49

Hope it helped

6 0

2 years ago

Hey I have a question. What is faithfulness in your opinion

Vsevolod [243]

Answer:

The quality of being faithful

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

1.

beks73 [17]

The commutative property of addition means the order of the addends doesn't matter; we get the same sum. In symbols

$a+b = b+a$

<span>11 + 7 = 7 + 11, choice B, is a good illustration of commutativity.

The next part asks us to use the commutative property. Looking at the choices, we see it's not the commutative property of addition we're to use, it's the commutative property of multiplication. Let's write that generally first:

</span> $ab = ba$

Applying that, <span>(4 + 7) * 3 = 3*(4+7), again choice B.
</span>

3 0

2 years ago