We wish to modify the cellular telephone coding system in order to reduce the number of errors. In particular, if there are two or three zeroes in the received sequence of 5 bits, we will say that a deletion (event D) occurs. Otherwise, if at least 4 zeroes are received, then the receiver decides a zero was sent. Similarly, if at least 4 ones are received, then the receiver decides a one was sent. We say that an error occurs if either a one was sent and the receiver decides zero was sent or if a zero was sent and the receiver decides a one was sent. For this modified protocol, what is the probability P[E] of an error? What is the probability P[D] of a deletion?

Answers

Answer 1

Solution :

Here, we have 5 trails that corresponds to the 5 times the binary symbol is sent. On each trail, success is said to occur when the binary symbol is received correctly. The probability of a success is p = 1 - q = 0.9 and q = 0.1

Now if the 0 is being transmitted, then the 0 is sent 5 number of times and then we call the decoding a 0 success. Let the repeated transmission are independent. In this case, we have 5 trails. Let each repeated bit the receiver decodes as 1 a success, using the binomial probabilities. We using the [tex]$S_{k,5}$[/tex] to denote an event of [tex]$k$[/tex] successes in the 5 trails, then the probability k are decoded at the receiver is:

[tex]$P[S_{k,5}]=\binom{5}{k}p^k(1-p)^{5-k}$[/tex]

           [tex]$=\binom{5}{k}(0.9)^k(1-0.9)^{5-k}$[/tex]

           [tex]$=\binom{5}{k}(0.9)^k(0.1)^{5-k}$[/tex]    

Here, k = 1, 2, 3, 4, 5

The probability of the transmitted bit to be decoded correctly is:

[tex]$P[C]=P[S_{5,5}]+P[S_{2,5}]$[/tex]

         [tex]$=\binom{5}{3}(0.9)^5(0.1)^{0}+\binom{5}{4}(0.9)^4(0.1)^1$[/tex]

         [tex]$=(0.9)^5+5(0.9)^4(0.1)^1$[/tex]

         = 0.91854

The probability that the deletion occurs is

[tex]$P[D]=P[S_{3,5}]+P[S_{2,5}]$[/tex]

          [tex]$=\binom{5}{3}(0.9)^3(0.1)^{2}+\binom{5}{2}(0.9)^2(0.1)^3$[/tex]

         [tex]$=10(0.9)^3(0.1)^2+10(0.9)^2(0.1)^3$[/tex]

         = 0.081

The probability of an error is

[tex]$P[E]=P[S_{1,5}]+P[S_{0,5}]$[/tex]

          [tex]$=\binom{5}{1}(0.9)^1(0.1)^{4}+\binom{5}{0}(0.9)^0(0.1)^5$[/tex]

         [tex]$=5(0.9)^1(0.1)^4+(0.1)^5$[/tex]

         = 0.00046


Related Questions

The chords intersect at point U.

A circle is shown. Chords R T and Q S intersect at point U. The length of R U is 12 centimeters, the length of U T is 4 centimeters, the length of U S is y centimeters, and the length of Q U is 8 centimeters.

What is the value of y?

2
4
6
8

Answers

Answer:

Its b)6

Step-by-step explanation:

I just did it on edge and got it correct

The value of y is 6 centimeters.

Given that,

The length of RU = 12 centimeters

The length of UT = 4 centimeters

The length of QU = 8 centimeters.

The length of US = y centimeters

What is the intersecting chords theorem?

The intersecting chords theorem states that, the product of one whole chords segment and its external segment is equal to the product of the other whole chords segment and its external segment when two chords cross at an exterior point.

According to the intersecting chords theorem,

US x QU = RU x UT

Substitute the values in above formula,

y x 8 = 12 x 4

y = 48/8

y = 6 centimeters,

Hence, the value of y is 6 centimeters.

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I need help with these answers?

Answers

Q 7 = 6

Q 8= -x + 2

Q 9= 6m + 2

Q 13= 43f × 56

Q 15= 18x

HELP PLSS- okok so i need the answer to this, please help :(

Answers

Answer:

second

Step-by-step explanation

-5/12 because -2/3 + 1/4 = -5/12

Answer:

2nd one

Step-by-step explanation:

Find value of x
Find value of y

Answers

Answer:

Step-by-step explanation:

use  SOH CAH TOA

Sin = Opp / Hyp

Cos = Adj / Hyp

Tan = Opp / Adj

then we know the adjacent side and the angle, and want to find the Hyp, so use  CAH

Cos(60) = ( 8[tex]\sqrt{3}[/tex]  / 3 ) / Hyp       ( cos(60) = 1/2 )

Hyp = (8[tex]\sqrt{3}[/tex] / 3) / (1/2)

Hyp = 2 ((8[tex]\sqrt{3}[/tex] / 3)

Hyp = 16[tex]\sqrt{3}[/tex] / 3

x =  16[tex]\sqrt{3}[/tex] / 3

Now use SOH

Sin (60) = Opp / 16[tex]\sqrt{3}[/tex] / 3      ( sin(60) = [tex]\sqrt{3}[/tex]/2 )

(16[tex]\sqrt{3}[/tex] / 3)([tex]\sqrt{3}[/tex]/2) = Opp

16 * 3 / 6  = Opp

8 = Opp

y = 8

:)

Damian took out a car loan for $10,500 that has a 0% APR for the first 12
months and will be paid off with monthly payments over 3 years. For how
many months will Damian be charged interest?
O A. 12 months
O B. 48 months
C. 36 months
O D. 24 months

Answers

24 months is the correct answer

Damian will be charged interest for 24 months.

What is unit conversion?

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are given that Damian took out a car loan for $10,500 that has a 0% APR for the first 12 months and will be paid off with monthly payments over 3 years.

We know that;

1 year = 12 months

Using this conversion we get;

3 year = 36 months

It means total number of months in 3 years is 36. For first 24 months the APR is 0%. So, the number of months will Damian be charged interest is

36 - 12 = 24

Therefore, the correct option is D. 24 months

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If a new sweater sells for $53 find the total cost if you are charged 5% sales tax. Round your answer to the nearest cent

Answers

Answer:

$55.65

Step-by-step explanation:

you would find 5% of 53 which is $2.65 and then add that to your original price so 53 + 2.65 = 55.65

What is the mean of the data set 85 97 84 88 95 81

Answers

Answer:

88.3 (3 is repeating)

Step-by-step explanation:

to calculate the mean of a data set you add together all the numbers and then divide that by the number of numbers there are, sorry if that's confusing

example:

85+97+84+88+95+81=530

530/6=88.3

Answer:

d .88

Step-by-step explanation:

hope this helps

which of the following can be written as the sum of 2 prime numbers

a)11
b)15
c)17
d)23
e)29

Answers

Answer:

b)15

Step-by-step explanation:

13+2=15

Hope that helps

B would be the answer

i need help on this question for my math homework:))) please help!

Answers

Ummyrhrbs here Susie whack

Solve for x and find the measure of Angle D.
A
(6x + 1)
(4x + 15)
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Angle D =
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Answers

ficidiie. ducisiie. dicidie. divodie

please help me im so confused​

Answers




This is the answer I got

Is 10 the solution of the equation 4x - 8 = 31?

Answers

4x-8 = 31

4x = 31 + 8

4x = 39

x = 9.75
4x - 8 = 31
4x = 39
x = 9.75

Solve the given proportion.
x/2=8/4
x=

Answers

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Find the value of x and y in the diagram below.
30°
A. x=9f2, y=9
B. * = 18, y = 9-3
C. *= 9/3, y = 4.5
D. *- 01/3, y = 313
Please select the best answer from the choices provided

Answers

Answer:

C. *=9/3,y=4.5 HOPE IT WILL HELP YOU

Answer: D

Step-by-step explanation: right on edge

how do movement skills in volleyball transfer to tennis?​

Answers

Answer:

Tennis – It's not difficult to see that tennis and volleyball have their similarity; both involve hitting a ball over the net in the hope that the opponent won't be able to return it. Much like tennis, volleyball requires short and explosive movements and cat-like reflexes, rather than long runs down a pitch.

20 divided 16 in fraction form (simplist form)

Answers

Answer:

1/4

Step-by-step exp

20/16=1.25=1/4

The fraction 20 divided by 16 can be expressed in simplified form as 5/4.

What is 20 divided 16 in fraction form?

To simplify the fraction 20 divided by 16, we need to find the greatest common divisor (GCD) of the numerator (20) and the denominator (16) and divide both by that number. Let's break down the steps:

Step 1: Find the GCD

To find the GCD of 20 and 16, we can use the Euclidean algorithm. We start by dividing 20 by 16, which gives us a quotient of 1 and a remainder of 4. We then divide 16 by 4, resulting in a quotient of 4 and no remainder. The last nonzero remainder obtained is 4, so the GCD of 20 and 16 is 4.

Step 2: Divide by the GCD

To simplify the fraction, we divide both the numerator and denominator by the GCD of 4.

20 ÷ 4 = 5

16 ÷ 4 = 4

So, the simplified fraction is 5/4.

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Find the quotient. Express the remainder as a decimal.

Answers

Answer:

no  rubdvghwcuebhc vn2egchgvsbjhcekdnax dj

Step-by-step explanation:ncvjhdrbecjfv n

Write the word sentence as an inequality. Then solve the inequality.
The quotient of a number g and -4 is at most 5 .

Answers

Answer:

g≥-20

Step-by-step explanation:

The quotient of a number g and -4 is expressed as;

g/-4

If the quotient of a number g and -4 is at most 5, this is expressed as;

g/-4 ≤ 5

Multiply both sides by -4

g/-4 * -4 ≤ 5 * -4

g *  ≥ -20

Hence the required solution is g≥-20

Divide. Write your answer as a decimal.

0.459 divided by 0.17 =

Answers

Answer:

0.459 divided by 0.17 equals 2.7

Step-by-step explanation:

Answer:

2.7

Step-by-step explanation:

0.459÷0.17=2.7

here is your answer!

If a=35, find the value of X.

Answers

Answer:

cCompute the value of x if angle a=35 ° angle b=45° angle c=50°. 2. See answers. Log in to add comment. Answer. 2.3/5. 2. 123jiya73. Helping ...

Use the net as an aid to compute the surface area of the triangular prism.

Answers

Answer: [tex]790m^{2}[/tex]

Step-by-step explanation: See image

Express this as a difference: 7+3 PLEASE HELP

Answers

Answer:

Step-by-step explanation:

How do you solve this problem

Answers

Answer:

V=[tex]8y^{15} ft^3[/tex]

Step-by-step explanation:

The volume of a cube is l*w*h, and since l,w,h are all the same multiply [tex]2y^5[/tex] by itself thrice and use exponent rules, which looks like this:

[tex](2y^5)^3\\(2)^3(y^5)^3\\8y^{15}[/tex]

If this helped, a brainliest would be greatly appreciated!

This need 2 answers whoever does it correctly get the best answer brainlyist

Answers

Answer:

A for sure. I want to say D is the other one

Step-by-step explanation:

the correct answer is A

The graph of a twice differential function is shown at right. Which of the following is true?

Answers

Answer:

(C)

Step-by-step explanation:

looking from the slope: f'(2) is negative

f(2)=0

the curve concave upward: f''(2) is positive

f'(2)<0

f(2)=0

0<f''(2)

f'(2)<0<f''(2)

The expression which is true n the graph of a twice differential function is f' (2) < 0 < f'' (2) so, option C is correct.

What is a differential function?

A function that has a derivative at each point in its domain is referred to as a differentiable function of one real variable in mathematics. In other words, each interior point in the domain of a differentiable function's graph has a non-vertical tangent line.

Given:

The coordinate of the graph is shown in figure  (2, 0),

As we can see from the graph, the slope: f' (2) is negative (Downwards)

Again, from the graph

f(2) = 0

Thus, the curve concave upward: f'' (2) is positive (upward)

f' (2)<0

f (2)=0

0 < f'' (2)

f' (2) < 0 < f'' (2)

Therefore, f' (2) < 0 < f'' (2) is true in the given graph.

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The monthly rents (in dollars) paid by 9 people are given below. 845,865,880,945,955,995,1020,1040,1140 Suppose that one of the people moves. His rent changes from $845 to $890. What happens to the mean?
what happened to the median?

Answers

Answer:

The mean goes up but the median remains the same

Step-by-step explanation:

845,865,880,945,955,995,1020,1040,1140

mean: 965

median: 955

865,880,890,945,955,995,1020,1040,1140

mean: 970

median: 955

Brittany has 5 pages of homework to do. If she can finish 1/5 of a page in one hour, how many hours will her homework take?

Answers

Answer:

25

Step-by-step explanation:

Which expression is NOT equivalent to −6×(13+13)? −63+13 −6×23 −6×(2×13) (13+13)×(−6)

Answers

Answer:

I know that -63+13= -50

(-6) * 23 = (-138) are NOT equivalent, the only expressions that are equivalent are (13+13)x(-6) and -6x(2x13) they both equal to -156 which is to say -6x(13+13) Are the same

Step-by-step explanation:

Which is better buy: 4 for $2.00 or 6 for $2.50

Answers

Answer:

6 for 2.50

Step-by-step explanation:

find the price of one for both
$2.00 divide by 4 is $0.5
$2.50 divide by 6 is $0.42

so 6 for $2.50 is a better buy

Angela is helping her father paint a fence. She can paint 3 sections of the fence in 25 minutes. How many minutes will it take Angela to paint 12 sections of this fence? ​

Answers

Answer:

100 Minutes.

Step-by-step explain:

25 divided by 3 = 8.33333333333, So, 8.3 minutes to paint one section at a time. So, 8.3 x 12 = 99.6. So, 99.6 rounded since the last number is higher than 5 it would go to the next number. So, rounded its 100 minutes.  100 minutes for Angela to paint 12 sections.

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