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A box contains 50 balls that are numbered from 1 to 50 and each ball has a different number. The balls numbered 1 to 22 are red. The balls numbered 23 to 40 are white. The balls numbered 41 to 50 are blue and white striped. One ball will be selected at random from this box. Are the outcomes equally likely? How do you know this?

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Karol E.
Karol E.Lv8
29 Mar 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

2 (a) Suppose you start with one Red and one Black ball in a bag. You draw a ball at random from the bag repeatedly and look at its colour each time. After each successive draw, you double the number of Red balls and triple the number of Black balls in the bag before the next draw (eg. on the third draw there will be 4 Red and 9 Black balls in the bag). Explain why you will draw only finitely many Red balls in total with probability 1. [3 marks]

(b) In a modified game, suppose instead that for before the nth draw, you first make an n by n square arrangement of balls where the perimeter balls are all Red and any interior balls are Black ball. Thus, on the second draw there are 4 Red and 0 Black in the bag (22 in total), on the third draw there are 8 Red and 1 Black in the bag (32 in total), on the fourth there are 12 Red and 4 Black in the bag (42 in total), and so on. How many Red and Black balls will there be on the nth draw? Will you still draw only finitely many red balls? Explain your answer. [4 marks]

A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make n guesses sequentially, where the ith one is a guess of the card in position i. Let N denote ht number of correct guesses. (a) If you are not given any information about your earlier guesses show that, for any strategy, E[N]=1. (b) Suppose that after each guess you are shown the card that was in the position  in question. What do you think is the best strategy? Show that, under this strategy.

 

(c) Suppose that you are told after each guess whether you are right or or wrong. In this case, it can be shown that the strategy which maximizes  E[N] is one that keeps on guessing the same card until you are told you are correct and then changes to a new card. For this strategy, show that 

 

Hint: For all parts, express N as the sum of indicator Hint: For all parts, express N as the sum of the indicator.

 

Opeele Kyinkafa sells different used 2005 GM cars in excellent condition. The value or the retail price (Price) of a car is dependent on a variety of characteristics such as number of miles the car has been driven (Mileage), manufacturer of the car (Make) such as Buick, Cadillac, Chevrolet, Pontiac, SAAB, and Saturn. The car price is also influenced by the body type (Type) such as sedan, convertible, coupe, hatchback and wagon. It is also affected by number of cylinders (Cylinders) in the engine, the engine size (Liter), cruise control which is an indicator variable representing whether the car has cruise control (yes) or no otherwise and Sound indicator representing whether the car has upgraded speakers (yes) or no otherwise. All cars in this data set were less than one year old when priced and considered to be in excellent condition. Determine which major variables are dummies and are dynamic? Identify 3 potential unobserved heterogenous factors in this dataset. Display the full descriptive statistics of the data in R. Why do you think some variables are starred (*)? What is the median for “price”, standard deviation for “mileage”, skewness for “cylinder” and mean for “sound”? Test if “price” is normally distributed using histogram, kernel density plot and the shapiro wilk test. Create a red scatterplot matrix of price, mileage, cylinder, liter, make. From your graph, is the correlation between price & mileage positive or negative? What’s the pearson correlation coefficient between price & mileage and between “cylinder” & “liter” correct to 2 d.p Create a correlation matrix of the dataset by finding the apt R command for converting all string/dummy variables From the matrix, identify 2 potentially good predictors? Identify 3 pairs of variables that are mostly multicollinear. Which 2 pairs of variables are least correlated? Identify 3 pairs of variables most highly correlated with Cylinder Generate a simple regression plot of price on mileage with a re fitted line. Run the whole multiple regression model (label the equation as "regprice") & use it to answer the other questions. Specify the regression model for the whole data keeping the exact names of the variables. Write the estimated regression equation. In one sentence, which variables are significant and which are not? Justify Is the regression model justifiable? Explain Interpret the coefficient of Mileage, MakeCadillac, TypeSedan, Cylinder, & Cruiseyes. Compare the price of a car with 130,000 mileage, 6 cylinders, 3.8 liters, with cruise and sound, was manufactured by Pontiac with a convertible body type with that of the price of a car with four cylinders, 120,000 mileage, 3.8 liters, without cruise nor sound, was manufactured by Cadillac with a hatchback body type. Which factor(s) appears to be causing a comparative difference (if any)? Using only the VIF, which one of the pairs of variables selected to be multicollinear may be deleted? Justify?

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