A lottery game works as follows: You have to pick 4 integers (without replacement) between 1 and 14(inclusive). The lottery operator chooses 4 numbers (without replacement) between 1 and 14 (also inclusive).If exactly two of the numbers you have chosen are among the four chosen by the operator, you win $ 10; ifexactly three of the numbers you have chosen are among the four chosen, you win $ 100; if all four of yournumbers match you win $ 1000. Otherwise, you have to pay $ 75. A random variable X represents your profit.(a) Complete the probability distribution of X, your profit resulting from playing this game, listing fromsmallest to largest. For each probability use four decimals in your answer.XP(X= x)(b) Sketch the distribution of probabilities from (a), with the values of X on the x-axis-and P(X) on the y-axis. What can you say about the tendency of the random variable X?The distribution of X is ?(c) Compute the expected value of X and the standard deviation of X.E(X) =SD(X) =(use two decimals in your answer)(use two decimals in your answer)

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Shawn is playing a game with a set of cards. Half of them are blue and the other half are yellow. In the game, the player guesses the color of the top card, looks at the card, and returns the card to the deck. The player continues to do this, shuffling the deck after each guess. Shawn has guessed the first three attempts as "blue” and has been correct on each guess. He says he will guess "yellow” for the next card since a yellow card is due to happen. Is Shawn’s reasoning correct? Yes, Shawn has guessed well so far, so it is clear that he cannot miss. No, all of the cards have been blue so far, so the next one must also be blue. Yes, half of the cards are yellow, so the fourth card should be yellow to compensate for the first three cards being blue. No, the law of large numbers says that the proportion of yellow cards should approach the true probability after many trials.
For a Halloween party, each guest can choose from the 6 different kinds of candy to have in a prize bag. If any number of candy types can be chosen, how many candy type combinations are possible?
A technology store holds a contest to attract shoppers. works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the ace. The person wins $100 of store credit if the ace is the first card, $50 if it is the second card, and $20, $10, or $5 if it is the third, fourth, or last card chosen. What is the average dollar amount of store credit given away in the contest? Estimate with a simulation of 10 trials. Once an hour, someone at checkout is chosen at random to play in the contest Here's how it 67819 00354 91439 91073 49258 15992 41277 75111 67496 68430 09875 08990 27656 15871 23637 00952 97818 64234 50199 05715
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 15 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 8 spots labeled $1, 16 spots labeled $2, and 1 spots labeled $10, how much should a player expect to win on average?
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 11 spots labeled $1, 10 spots labeled $2, and 5 spots labeled $10, how much should a player expect to win on average?
Toward the end of a game of Scrabble you hold the letters D,O,G and Q. You can choose three of these four letters and arrange them in order in how many different ways?
You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Here are the rules of NALGO: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. Your final score is the number of cards that are placed on the table. For example, if n = 3, then there are six possible scenarios, each of them equally likely to occur. The cards placed on the table are marked in bold. First Card Second Card Third Card 1 2 3 1 3 2 2 2 3 3 1 3 1 2 3 1 2 1 Cards on Table 1, 2, 3 1, 3 2 2, 3 3 3 Points 3 2 1 2 1 1 Thus, if there are n = 3 cards in the deck, then you score 1 point with probability , 2 points with probability, and the maximum 3 points with probability. And so, the expected value of…
You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. ***The image is the example*** Questions: Prove that for all positive integers n ≥ 3, if there are n cards in the deck, you score exactly 1 point with probability 12 and exactly 2 points with probability 13.
Suppose that nine children are sitting in a row. When the music starts, they get up and run around the row of chairs. When the music stops they each sit in an empty chair. In how many ways can it happen that none of them are sitting in the original chair that they occupied at the start of the game? Use an approximation for your answer and round it to the nearest whole number.
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 13 spots labeled $1, 15 spots labeled $2, and 7 spots labeled $10, how much should a player expect to win on average?

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