Knowee
Questions
Features
Study Tools

Suppose that the output of a process that generates independent symbols {A, B, C, D, E} with known probabilities {in the same order: 0.2, 0.33, 0.1, 0.07, 0.3 } needs to be communicated. What is the entropy (bits/symbol)? (Your answer should be rounded off to the nearest first decimal point. Type a number only - no units.)

Question

Suppose that the output of a process that generates independent symbols {A, B, C, D, E} with known probabilities {in the same order: 0.2, 0.33, 0.1, 0.07, 0.3 } needs to be communicated. What is the entropy (bits/symbol)? (Your answer should be rounded off to the nearest first decimal point. Type a number only - no units.)

🧐 Not the exact question you are looking for?Go ask a question

Solution 1

To calculate the entropy (H) in bits/symbol for a source that generates independent symbols with known probabilities, we use the formula:

H = - ∑ [ p(i) * log2 p(i) ]

where p(i) is the probability of each symbol.

Let's calculate:

H = - [ (0.2 * log2 0.2) + (0.33 * log2 0.33) + (0.1 * log2 0.1) + (0.07 * log2 0.07) + (0.3 * log2 0.3) ]

Now, calculate the log2 of each probability and multiply by the probability:

H = - [ (0.2 * -2.32) + (0.33 * -1.59) + (0.1 * -3.32) + (0.07 * -3.85) + (0.3 * -1.74) ]

H = - [ -0.464 + -0.5253 + -0.332 + -0.2695 + -0.522 ]

H = - [ -2.1128 ]

H = 2.1128

So, the entropy is approximately 2.1 bits/symbol when rounded off to the nearest first decimal point.

This problem has been solved

Solution 2

To calculate the entropy (H) in bits/symbol, we use the formula:

H = - ∑ P(x) * log2(P(x))

where P(x) is the probability of each symbol.

Let's calculate:

H = - [0.2log2(0.2) + 0.33log2(0.33) + 0.1log2(0.1) + 0.07log2(0.07) + 0.3*log2(0.3)]

Now, calculate the log2 of each probability and multiply it by the probability itself:

H = - [0.2*(-2.32) + 0.33*(-1.59) + 0.1*(-3.32) + 0.07*(-3.85) + 0.3*(-1.74)]

H = - [-0.464 -0.5253 -0.332 -0.2695 -0.522]

Now, add all these values together:

H = - [-2.1128]

Finally, remove the negative sign:

H = 2.1128

Rounding off to the nearest first decimal point, the entropy is 2.1 bits/symbol.

This problem has been solved

Solution 3

To calculate the entropy (H) in bits/symbol, we use the formula:

H = - ∑ P(x) * log2(P(x))

where P(x) is the probability of each symbol.

Let's calculate:

H = - [0.2log2(0.2) + 0.33log2(0.33) + 0.1log2(0.1) + 0.07log2(0.07) + 0.3*log2(0.3)]

H = - [(-0.46438561897747244) + (-0.5287712379549449) + (-0.33219280948873625) + (-0.2630344058337938) + (-0.5210896782498619)]

H = 2.1094737418048093

So, the entropy is approximately 2.1 bits/symbol when rounded off to the nearest first decimal point.

This problem has been solved

Similar Questions

Consider a process that generates a set of symbols with a known probability distribution. We calculate the entropy assuming that the symbols are IID (Independent and Identically Distributed), but then discover that there are certain relationships between the symbols that mean they are NOT truly independent. Compared with our first calculation, would you expect that the true entropy is actually Question 6Select one:

Suppose we receive a series of 8-bit words representing some symbols or event outcomes, and we notice that, on average, about 70% of the received bits are “1”, and only 30% are “0”. What, if anything, does that tell us from an information theoretic point of view? Question 2Select one: Nothing. We would need to know the probability of received words before we could calculate the entropy. Since 1 and 0 are not equi-probable, we know that we could send the sequence of symbols with fewer bits using a suitable code word assignment method. Plugging the probabilities into the information theory equations would give us the optimum encoding method we should use. (JUST choose the right option)

Suppose that the output of a process that generates independent symbols {A, B, C, D, E} with known probabilities {in the same order: 0.2, 0.33, 0.1, 0.07, 0.3 } needs to be communicated. If we constructed a Huffman code to represent the symbols, what would be the average number of binary digits/symbol that would result? (Your answer should be accurate up to the first decimal point. Type a number only - no units.)

Time left 0:32:25Question 6Answer savedMarked out of 2.00Flag questionTipsQuestion textConsider a process that generates a set of symbols with a known probability distribution. We calculate the entropy assuming that the symbols are IID (Independent and Identically Distributed), but then discover that there are certain relationships between the symbols that mean they are NOT truly independent. Compared with our first calculation, would you expect that the true entropy is actuallyQuestion 6Select one:reducedincreasedunchangedunknownClear my choiceQuestion 7Answer savedMarked out of 2.00Flag questionTipsQuestion textWhich of the following variable length code word sets is a prefix code (meaning that no code word is a prefix of another code word)?Question 7Select one:{ 1010, 1001, 1011, 01001, 10010, 10101 }{ 0, 10, 110, 1110, 1111 }{ 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, 100, 101, 110, 111 }{ 0, 10, 101, 110, 100 }Clear my choiceQuestion 8Answer savedMarked out of 2.00Flag questionTipsQuestion textIn terms of block data and stream data, which of the following statements is true about video communications?Question 8Select one:Video communications becomes stream data only when there is associated audio. A video message or movie transferred as a file is block data, while video that is decoded and displayed continuously as it arrives is stream dataAll video communications is block dataAll video communications are stream dataClear my choiceQuestion 9Answer savedMarked out of 2.00Flag questionTipsQuestion textA low-pass analogue signal has a bandwidth of 15 kHz and has a SNR of 43 dB due to thermal noise and interference from nearby electrical equipment. If uniform 10-bit quantisation is used when sampling and digitising the signal, which of the following would you expect to be the output digital bit rate?Question 9Select one:75 kbit/s150 kbit/s100 kbit/s30 kbit/s330 kbit/s

Define Entropy

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.