Suppose we have 4 outcomes of the paired events of flipping a coin and drawing one of two cards (one red, one black). So, the four events are head/red, tail/red, head/black, tail/black. If it is a fair coin, the red and black cards are drawn with equal probability and the two events (coin toss and card draw) are independent, what is the entropy per outcome?

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:

Two fair coins are tossed. Let A be the event that the first coin displays a heads, and let B be theeven that both coins display the same outcome.(a) Are events A and B mutually exclusive?(b) Are events A and B independent?2) A card is drawn from a standard deck of 52 cards. Let A be the event that an ace is drawn and let Bbe the event that a spade is drawn.(a) Are these events mutually exclusive or non-mutually exclusive? Explain your answer.(b) Calculate the probability of event A or event B occurring (drawing an ace or a space).A dice is tossed after a card is drawn. Let C be the event that an even number is shown on the dice.(c) Are events A and C independent or non-independent?(d) Calculate the probability of events A and C occurring (drawing an ace and rolling aneven number).3) Given that
 ∪  = 0.7 and
 = 0.2, find
 and
 ∩  if:(a) A and B are mutually exclusive(b) A and B are independent4) Two dice are rolled and the sum is recorded.(a) List all possible outcomes (i.e. the sample space).(b) Calculate the probability of rolling:(i) A sum of 5(ii) A sum of 4 or less(iii) A sum of at most 11(iv) A sum that is a multiple of 3 or a multiple of 4.5) 200 people attended a blood bank and their blood types are recorded as follows: 50 have type A,65 have type B, 70 have type O and 15 have type AB.(a) Calculate the relative probability of each blood type.(b) If two people are selected without replacement, what is the probability that:(i) One person is type A and the other is type B.(ii) They both have type B blood.(iii) They both have the same type blood.6) A coin is tossed three times and the results are recorded. What is the probability of getting:(a) Three heads.(b) At least two heads.(c) At most one tail.STAT6010 27) Two unfair coins are tossed with the probability of a tail equal to 0.25. Calculate the probability ofgetting:(a) No heads.(b) Exactly one head.(c) At least one head.8) An urn contains 6 black balls, 4 white balls and 5 red balls. The balls are removed 1 at a time fromthe urn and not replaced. If 3 balls are removed, what is the probability that:(a) All three are red.(b) Two are black and one is white(c) All are the same colour(d) At least 1 is white9) 70% of houses in a residential area have an alarm. It is found that 35% of the owners of thealarmed houses have a dog and 42% of the owners of the non-alarmed houses have a dog.a) Construct a tree diagram to show all possible events and probabilities.b) A house is selected at random. Calculate the probability that the house does nothave a dog.c) If a randomly selected house is one of the houses that does not have a dog, what isthe probability that the house has an alarm?10) On any given day, the probability that an employee will drive to work is 0.5, the probabilitythat he/she will cycle to work is 0.3 and the probability that he/she will walk to work is 0.2.If he/she drives, the probability that he/she will arrive on time is 0.6 If he/she cycles, theprobability that he/she will arrive on time is 0.8. If he/she walks, the probability thathe/she will arrive on time is 0.9. An employee is selected at random.a) Calculate the probability that the employee will arrive on time for work.b) If the employee has arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.c) The employee has not arrived on time for work yesterday. Calculate the probabilitythat he/she walked to work yesterday.

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.)

How many different possible outcomes are there if you flip four coins?

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