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Q: please send handwritten solution for Q3 part 1
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- Vx (-y +2,22 +323, 2233) =? 0 (3y -3222, 223, -2 + 2) 0 (-3y +3X372, -332, 1 + 2x) 0 (2y +2224-423,1 + 22) 0 (-34-3222, 42,1 +22) 0 (-3y +322y2, -3'2, 1 + 2)Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y ?(Total number of times he roll the die is 4.)A family is coloring eggs and wants to make two shades of purple, “light purple” and “deep purple”. They have 30 tablespoons of red solution and 2 tablespoons of blue solution. If “light purple” consists of 2% blue solution, and “deep purple” consists of 10% blue solution, how much of each version of purple solution can be created? Let x represent thenumber of tablespoons of “light purple” to be created, and let y represent the number of tablespoons of “deep purple”. Based on the information provided, the two tablespoons of blue solution will be distributed according to the following linear equation. 2 = ? x + ? y Complete the equation above by filling in the boxes, then write a similar linear equation that shows the distribution of the red solution. Solve the resulting system of linear equations.
- A particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.Maximize B=5xy^2, where x and y are positive numbers such that x+y^2=5.Suppose 55 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Yes No
- At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 50 + z + u and x − y + z − u = 58. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo GoogleConsider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.Suppose 60 percent of the customers at Pizza Palooza order a square pizza, 80 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?
- A fast food company is offering a prize promotion game. The company claims that in 0.5 % of all orders will receive $100 cash1% of all orders will receive $ 10 cash and 10\% of orders will receive a coupon for a free soft drink. The remaining orders will receive no prizes. A group of long- time customers were excited about the new promotion, and over the course of the promotion, they placed 651 ordersOf these orders, 2 ended up winning $100,6 won $10 and 52 won a free soft drink. If this group wanted to do a chi-squared goodness of fit test to test the advertised odds, what would be the appropriate null and alternative hypotheses?At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 12 x + y = 44 + z + u and x − y + z − u = 36. How large was the audience of each of the four companies at the end of that year? Microsoft million Time Warner million Yahoo million Google millionSuppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza? Mutiple Choice:a. No b. Yes
