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# hmwk2 - (b Four of a kind(four cards with the same face...

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CSCI 5753 / 5753 Homework #2 Due Thuesday, Feb. 20th 1. Fred Poisson, the chief statistician in Disneyland, has found that 72% of the visitors go on the Jungle Cruise, 56% ride the monorail, 60% take the Matterhorn ride, 50% go on the Jungle Cruise and ride the monorail, 45% take the Jungle Cruise and ride the Matterhorn, 40% take the monorail and ride the Matterhorn, 30% take all three rides. Assuming these values are correct, calculate the probabilty that a visitor to Disneyland will: (a) Go on at least one of the three rides (b) Ride the monorail given that the jungle cruise was taken (c) Take the matterhorn ride given that both the jungle cruise and the monorail rides were taken. 2. Find the probability of NOT drawing a pair in poker. You can still have a straight or ﬂush, etc, but not three or four of a kind. 3. Find the probability of getting each of the following poker hands: (a) A straight ﬂush (ﬁve cards in a sequence in a single suit, but not a royal ﬂush. Since an ace can also be thought of as a one, the sequence ace, 2, 3, 4, 5 in one suit is a straight ﬂush).
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Unformatted text preview: (b) Four of a kind (four cards with the same face value) (c) Full house (one pair and one triple of the same face value, such as ace, ace, king, king, king) (d) Flush (ﬁve cards in one suit but not a straight or royal ﬂush) (e) Straight (ﬁve cards in sequence, not all of the same suit) 4. (Graduate students only, or extra for undergrads) A single disk platter has N concentric tracks and one access arm. There is a uniform likelyhood of accessing any given track. The probability that a randomly chosen seek will take the arm to track i is p i . Let X represent the number of tracks passed between consecutive seeks, assuming no physical repositioning of the arm between seeks. Show the following: (a) X assumes the values 0 , 1 ,...,X n-1 and has the pmf deﬁned by p ( j ) = P [ X = j ] = ± ∑ N i =1 p i 2--( j = 0) 2 ∑ N-j i =1 p i p i + j--( j > 0) (b) For the case p i = 1 /N for all i , show it is true that E [ X ] = ( N 2-1) 3 N ≈ N 3 . 1...
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