1.-Consider a digital communication channel with the following error probabiliti

Question

1.-Consider a digital communication channel with the following error probabilities:

If a 0 is sent, a 1 is detected at the receiver with a probability of 0.1.

If a 1 is sent, the receiver detects a 0 with a probability of 0.05.  

Suppose that a packet of 0’s and 1’s is sent and 70% of the digits in this packet are 1.

Find the following:

(a) The percentage of 1’s in the received packet.

(b) The probability that a 0 was sent given that a 1 is received.

(c) The probability that a 1 was sent given that a 0 is received.

2. You have a fair fivesided die. The sides of the die are numbered from 1 to 5. Each die roll is independent of all others, and all faces are equally likely to come out on top when the die is rolled. Suppose you roll the die twice.

Consider the following events:  

A:  the total of two rolls is 10

B: at least one roll resulted in 5

C: at least one roll resulted in 1

(a) Calculate P[A], P[B], P[C].  

(b) Is event A independent of event B?  

(c) Is event A independent of event C?

Explanation / Answer

1)

a) percentage of 1's = 0.70

b) probability is 0.1 / 0.70 = 0.1429

c) probability is 0.05 / 0.70 = 0.0714

for the other question

I can gladly help you but you should post it in a new question

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