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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On a particularly boring transatlantic flight, one of the authors amused himself by counting the heads of the people in the seats in front of him. He noticed that all 28 of them either had black hair or had a whole row to themselves (or both). Of this total, 25 had black hair and 5 were fortunate enough to have a whole row of seats to themselves. How many of the black- haired people had whole rows to themselves? people
Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?
Dr. Lawrence has minimized his wardrobe during the fall of 2020, since there's no reason to dress up fancy these days. He has three pairs of jeans, five sweatshirts, and four hats that he puts to regular use. If he were to select his outfit for the day at random, how many different jean-sweatshirt-hat combinations are there? 6.
We have $20, given as 20 identical one-dollar coins (i.e. we have 20 loonies). Alex, James, and Peter are going to split the $20. We require that everyone gets at least 1 dollar. That is, everyone gets at least one loonie. In how many ways can we do this?
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In the local boating pond there are 10 plain wooden boats, each with a different number. The owner decides that some of these boats will be painted: one in blue, one in green, one in red, and one in orange, and the remaining ones left unpainted. How many ways are there to paint the boats? The number of ways is
Tyler was given the following counting problem to solve: “ You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one queen and at least one spade. He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades QA. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four cards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queen spade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades so that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes that the answer is 51C4 + (3 · 12 · 49C3). His answer is incorrect. Explain why, and give the correct answer.
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