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There is a total of 52 cards, e.g., no extra joker cards. In each event, you...

There is a total of 52 cards, e.g., no extra joker cards. In each event, you shuffle the deck of cards randomly, pick a card, and observe the suit and the rank.

  1. What is the information entropy value for one event?
  2. What is the entropy value for four events?
  3. Now suppose the face cards (the jack's, queen's, and king's) are considered the same as 10's. That is, jack's, queen's, and king's are effectively the same as 10's. What is the information entropy for one event?
  4. Now suppose you only consider the suit in the card-picking event (i.e., rank gets ignored and does not matter). What is the information entropy for one event?
  5. You can control and change the rank (but not the suit) of all the cards. How would you modify the deck of cards to minimize the information entropy? What is the resulting information entropy for an event after modifying the cards?
  6. You can change both the suit and the rank of the cards. How would you modify the cards to minimize the information entropy? What is the resulting information entropy for an event after modifying the cards?
Math   Statistics-And-Probability   
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