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Problem 3 (10 points). What are the expected value and variance of the number of full...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15 and p. (1) If p = 0.30, Find E(X + (n - X)). [Note that n-X is the number of failures). (2) Find p such that P(X = 6) is most probable. In other words, please find p = po such that P(X = 6) achieves at the maximum as a function of p at p = Po
Problem 6. (20 pts) By definition, a poker hand is a set of 5 cards from...
Problem 6. (20 pts) By definition, a poker hand is a set of 5 cards from a standard French deck of 52 cards1. Solve the following two problems (a) A poker hand is said to be a four of a kind if it has four cards with the same value. For instance, four sevens, four Queens or four Aces. Compute the prob- ability of drawing a four of a kind hand. (b) A poker hand is said to be a...
1. Find the probabilities of Poker hands not covered in class. Recall in a Poker game,...
1. Find the probabilities of Poker hands not covered in class. Recall in a Poker game, 5 cards are drawn uniformly at random from a deck of 52 cards. Each deck has 13 denominations ({A, 2, 3, . . . , 10, J Q, K)) and 4 suits (4,◇,0,6 ). In what follows consecutive denominations are But (J,Q,K, A, 21 is not considered consecutive. Find the probabilities of a. Straight Flush (5 cards of consecutive denomination, all of the same...
18. This is an excellent exercise for practicing counting. Find the number of f hands, dealt...
18. This is an excellent exercise for practicing counting. Find the number of f hands, dealt from a standard 52-card deck, that contain: (a) a royal flush (A-K-Q-J-10 all in one suit); (b) a straight flush (five cards of consecutive denominations all in one suit, but not royal flush); (c) four-of-a-kind (four cards of one denomination and one card of a different de nomination); (d) a full house (three cards of one denomination and t two of a different denomina...
1.How many possible orderings of letters ABCDEFG are there? 2.How many strings of length 4 can be made using the letters...
1.How many possible orderings of letters ABCDEFG are there? 2.How many strings of length 4 can be made using the letters ABCDEFG? 3.How many subsets of size 4 are there of the letters ABCDEFG. 4.How many possible strings are there of the letters "MATTER"? 5.Consider four books: an engineering book (E), a physics book (P), a history book (H), and an Art book (A). Consider the following problem: Suppose that the library has at least six copies of each of...
java programming 3. Back to contract bridge. The shape of the hand (that is, how "balanced"...
java programming
3. Back to contract bridge. The shape of the hand (that is, how "balanced" or "unbalanced" it is) is urposes as its raw point count. Write a method often just as important for the hand evaluation p public String bridgeHandShape(String hand) that creates and returns a four-element string that tells how many spades, hearts, diamonds and clubs, in this order, there are in the hand. This result string should contain these four counts in order separated by commas,...
C Programming The following code creates a deck of cards, shuffles it, and deals to players....
C Programming The following code creates a deck of cards, shuffles it, and deals to players. This program receives command line input [1-13] for number of players and command line input [1-13] for number of cards. Please modify this code to deal cards in a poker game. Command line input must accept [2-10] players and [5] cards only per player. Please validate input. Then, display the sorted hands, and then display the sorted hands - labeling each hand with its...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
ECS20: Discrete Mathematics UC Davis Instructor: Dale Fletter Student Name Here!!! Problem Set 3 Due September...
ECS20: Discrete Mathematics UC Davis Instructor: Dale Fletter Student Name Here!!! Problem Set 3 Due September 4, 2019, noon in homebox located 2131 Kemper Problem 1: (1 points) In the card game of poker, five cards that have consecutive kinds is called a straight An ace can be considered either the lowest card of an A-2-3-4-5 straight or the highest card of a 10 J-Q-K-A straight. What is the probability that a five-card poker hand contains a straight? For this...
Problem 4 (10 points). Let X be a binomial random variable with parameters n = 15 and p. (1) If p = 0.30, Find E(X + (n - X)). [Note that n-X is the number of failures). (2) Find p such that P(X = 6) is most probable. In other words, please find p = po such that P(X = 6) achieves at the maximum as a function of p at p = Po
Problem 6. (20 pts) By definition, a poker hand is a set of 5 cards from a standard French deck of 52 cards1. Solve the following two problems (a) A poker hand is said to be a four of a kind if it has four cards with the same value. For instance, four sevens, four Queens or four Aces. Compute the prob- ability of drawing a four of a kind hand. (b) A poker hand is said to be a...
1. Find the probabilities of Poker hands not covered in class. Recall in a Poker game, 5 cards are drawn uniformly at random from a deck of 52 cards. Each deck has 13 denominations ({A, 2, 3, . . . , 10, J Q, K)) and 4 suits (4,◇,0,6 ). In what follows consecutive denominations are But (J,Q,K, A, 21 is not considered consecutive. Find the probabilities of a. Straight Flush (5 cards of consecutive denomination, all of the same...
18. This is an excellent exercise for practicing counting. Find the number of f hands, dealt from a standard 52-card deck, that contain: (a) a royal flush (A-K-Q-J-10 all in one suit); (b) a straight flush (five cards of consecutive denominations all in one suit, but not royal flush); (c) four-of-a-kind (four cards of one denomination and one card of a different de nomination); (d) a full house (three cards of one denomination and t two of a different denomina...
java programming
3. Back to contract bridge. The shape of the hand (that is, how "balanced" or "unbalanced" it is) is urposes as its raw point count. Write a method often just as important for the hand evaluation p public String bridgeHandShape(String hand) that creates and returns a four-element string that tells how many spades, hearts, diamonds and clubs, in this order, there are in the hand. This result string should contain these four counts in order separated by commas,...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
ECS20: Discrete Mathematics UC Davis Instructor: Dale Fletter Student Name Here!!! Problem Set 3 Due September 4, 2019, noon in homebox located 2131 Kemper Problem 1: (1 points) In the card game of poker, five cards that have consecutive kinds is called a straight An ace can be considered either the lowest card of an A-2-3-4-5 straight or the highest card of a 10 J-Q-K-A straight. What is the probability that a five-card poker hand contains a straight? For this...
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