Question

In: Statistics and Probability

In a ternary (three level) communications system, 3 is transmitted three times more frequently than a...

In a ternary (three level) communications system, 3 is transmitted three times more frequently than a 1 while a 2 is transmitted two times more frequently than 1.

Probability of receiving a 2 when is 1 transmitted is α/2 (same for receiving a 3).

Probability of receiving a 1 when 2 is transmitted is β/2 (same for receiving a 3).

The probability of receiving a 2 when 3 is transmitted is γ/2 (same for receiving a 1).

(a) Draw the transition or the structure of the channel indicating the various probabilities

(b) At the receiver a '1' is observed. Using part (a) or directly, estimate the probability that the observed 1 was transmitted as a 1?

(c) Using parts (a), (b), or directly, what is the probability of receiving a 2' or a ‘3'?

Solutions

Expert Solution

(a) The transition diagram will look like this:

For example, when 1 is transmitted, the probability of receiving 1 is , the probability of receiving 2 is , and the probability of receiving 3 is also .

Also, let x be the probability of transmitting 1. Then, probability of transmitting 2 is 2x and the probability of transmitting 3 is 3x. So,

So, probability of transmitting 1, 2, and 3 are 1/6, 2/6 = 1/3, and 3/6 = 1/2 respectively.

(b) From the transition diagram, we can see that 1 can observed because of three transitions. So, P(1 was transmitted | 1 was observed) = P(1 was transmitted and 1 was observed) / P(1 was observed)

(c) Again, from the transition diagram, we can see that P(receiving 2 or 3)

= P(sending 1) * P(receiving 1 as 2 or 3) + P(sending 2) * P(receiving 2 as 2 or 3) + P(sending 3) * P(receiving 3 as 2 or 3)


Related Solutions

given a two-level atomic system where level-2 is more energetic than the ground state level-1, what...
given a two-level atomic system where level-2 is more energetic than the ground state level-1, what is the meaning of the expression       dN2/dt = B12uvN1 -B21uvN2-A21N2         when in thermal equilibrium show that     A21N2 + B21uvN2 = B21uvN1
There are over 5,000 banks in the United States—more than 10 times more per person than...
There are over 5,000 banks in the United States—more than 10 times more per person than in other industrialized countries. A recent study suggests that the long-run average cost curve for an individual bank is relatively flat. If Congress took steps to consolidate banks (merge some of the banks), thereby reducing the total number to 2,500, what would you expect to happen to average costs within the banking industry?
There are over 5,000 banks in the United States—more than 10 times more per person than...
There are over 5,000 banks in the United States—more than 10 times more per person than in other industrialized countries. A recent study suggests that the long-run average cost curve for an individual bank is relatively flat. If Congress took steps to consolidate banks, thereby reducing the total number to 2,500, what would you expect to happen to costs within the banking industry? Please provide a detailed explanation in terms of what long-run average cost curve for the individual bank...
There are over 5,000 banks in the United States—more than 10 times more per person than...
There are over 5,000 banks in the United States—more than 10 times more per person than in other industrialized countries. A recent study suggests that the long-run average cost curve for an individual bank is relatively flat. If Congress took steps to consolidate banks, thereby reducing the total number to 2,500, what would you expect to happen to costs within the banking industry? Please provide a detailed explanation in terms of what long-run average cost curve for the individual bank...
Under Obamacare older people can be charged up to three times more than younger people for...
Under Obamacare older people can be charged up to three times more than younger people for coverage under the same health insurance plan (this is described as a 3:1 cost ratio). True False
Do people under 40 defecate more than 3 times a day? I need to find a...
Do people under 40 defecate more than 3 times a day? I need to find a proper hypothesis testing and I am unsure of what data to actually use to construct the claim, NULL, ALT, SIGNIFICANCE LEVEL and appropiate test statistics. (AGE/TIMES PER DAY) 40 4 43 1 42 2 70 1 66 3 27 2 69 4 70 1 47 3 48 1 43 2 28 2 37 6 20 1 20 0 39 5 24 5 21 3...
much more frequently than this (that is OK and encouraged). After posting, make sure to return...
much more frequently than this (that is OK and encouraged). After posting, make sure to return several more times to the discussion to read more new posts and respond where appropriate. Post # 1: Write a short, well-written paragraph (maximum 5-8 sentences) that responds to this question: Please consult the chapter on International Trade in your textbook to review and learn about the comparative advantage, specialization based on comparative advantage, benefits of trade, trade barriers such as tariffs and quotas,...
Balding and color blindness are genetic mutations that occur more frequently in males than females. This...
Balding and color blindness are genetic mutations that occur more frequently in males than females. This is because its a _______________ trait recessive dominant sex linked polyploidy
Why might it be useful for a company to evaluate its prices more frequently than once...
Why might it be useful for a company to evaluate its prices more frequently than once per year? How might breakeven analysis help make it practical to carry out more frequent price evaluation?
Please be brief and no more than 3 sentences are expected. Why a good financial system...
Please be brief and no more than 3 sentences are expected. Why a good financial system is important for an economy? Do all the financial institutions’ functions are similar to each other? Explain “loanable funds market”? Is “saving” necessary for “investment”? How the government can influence the loanable funds market outcomes?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT