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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- Spring '11
- Playing card, disneyland, Magic Kingdom, Matterhorn Bobsleds, ﬁve cards, jungle cruise