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
chubhunter [2.5K]
3 years ago
9

A communication channel transmits a signal as sequence of digits 0 and 1. The probability of incorrect reception of each digit i

s p. To reduce the probability of error at reception, 0 is transmitted as 00000 (five zeroes) and 1, as 11111. Assume that the digits are received independently and the majority decoding is used. Compute the probability of receiving the signal incorrectly if the original signal is (a) 0; (b) 101. Evaluate the probabilities when p D 0:2.
Mathematics
1 answer:
prohojiy [21]3 years ago
3 0

Answer:

Probability of receiving the signal incorrectly is ".05792"

Step-by-step explanation:

Since it is mentioned here that the majority decoding is used so it implies that if the message is decoded as zero if there have been minimum of 3 Zeros in the messgae.

As we can see that there have been 5 bits, so the incorrection will occur only if there have been atleast 3 incorrect bits. Here we are asked to find out the probability of receiveing the signal incorrectly so i will take incorrectly transmiited bit as "Success".

The binomial distribution gives the probability of exactly m successes in n trials where the probability of  each individual trial succeeding is p.

With this method, we get the following pattern,

Binomial at (m=3, n=5, p=0.2) for probability of incorrection due to exactly 3 fails,

Binomial at (m=4, n=5, p=0.2) for probability of incorrection due to exactly 4 fails,

Binomial at (m=5 ,n=5, p=0.2) for probability of incorrection due to exactly 5 fails.

hence the probability "P" of receiving the signal incorrectly will be,

           P=(⁵₃) p³ (1 − p)⁵⁻³   +     (⁵₄) p⁴(1 − p)⁴⁻³      +      (⁵₅) p³(1 − p)³⁻³

whereas,

(⁵₃)= 5! / (5-3)! = 10

(⁵₄)= 5! / (5-4)! = 5

(⁵₅)= 5! / (5-5)! = 1

Putting these values in above equation we get,

P= 10 (0.2)³(1-0.2)²  + 5(0.2)⁴(1-0.2)¹  + (0.2)⁵

P=.05792

So the probablility "P" of receiving the signal incorrectly becomes ".05792"

You might be interested in
To which set does -1/2 belong? A whole numbers only B rational numbers only
Jlenok [28]

Answer:

B

Step-by-step explanation:

Because -1/2 is not a whole number so b is the only answer left

8 0
3 years ago
Read 2 more answers
How many square feet bigger is Figure A than Figure B?
Gemiola [76]
Figure A is 319.5 and figure B is 315 so I subtracted and got 4.5 so the answer is C
6 0
3 years ago
Read 2 more answers
Box A has a volume of 12 cubic meters. Box B is similar to box A. To create box B, box A's dimensions were multiplied by five. W
cestrela7 [59]

The formula for the volume of a box (assuming that it is in the shape of a cube) is <u>V=B^3</u>.

12=B^3

Now, do the cube root of 12 to find each dimension, all dimensions will be equal as it is a cube.

B= about 2.29 (when doing on a calculator keep full answer and do not round)

Now to find the volume of box B, multiply each dimension by 5

5(2.29...) times 5(2.29...) times 5(2.29...)

=1,500 m^3

Hope this helps!

3 0
3 years ago
Read 2 more answers
What are the slope and the y-intercept of the line shown in the graph?
Gelneren [198K]
Answer is A :) because it is rise over run
4 0
3 years ago
If the triangle ABC=JKL<br> and <br> ACB=12,KL=6cm,and AC=8.5cm<br> what is BC
Illusion [34]
BC is equal to KL so there for BC is 6 cm
5 0
3 years ago
Other questions:
  • An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 4 cm long. A second side of the
    13·1 answer
  • Consider the function f(x)=x^2-5. If g(x)=f(x-7), what can be said about g(x)? check all that apply
    11·1 answer
  • What are the building blocks of geometry?
    9·1 answer
  • Triangle IJK, with vertices I(-9,-8), J(-5,-6), and K(-7,-3), is drawn on the coordinate grid below.
    10·1 answer
  • Cual es la diferencia entre divisor y divisible
    14·1 answer
  • Cans someone please help me
    12·2 answers
  • El precio de la tortilla aumentó 50% en el primer mes. ¿Qué fracción corresponde con este aumento?​
    9·1 answer
  • (20 PTS) Preform the indicated questions, then answer the question!
    6·1 answer
  • Please help, I’ll mark your answer as brainliest!
    15·1 answer
  • Most people can walk about 3750 feet in 15 minutes what is the unit rate in feet per minute for this walking pace
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!