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

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"

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.

its 60

4 x 12 = 48

3 x 4 = 12

48 + 12 = 60

yeeeet