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Problem 1: There is an unlimited pile of balls. They are numbered by 1, 2, 3....... Two players A and B randomly select one ball each and check their number. The winner is the player who picked the lowest numbered ball. Let us consider the chances of winning of player A. Assume that player A picked a ball with number k. As there is a finite number of balls numbered lower than k and unlimited number of ball with larger numbers, then we can conclude that the chance of player A winning is much more likely than loosing. However, the same argument works for the player B. Thus, both players have advantage over the other player. How is it possible?
Problem 2: Think of 10 cups with 1 marble in the first cup, 2 marbles in the second cup, 3 marbles in the third cup, and so on. Show that if cups are arranged in a circle in any order, then some three adjacent cups in the circle must contain a total of at least 17 marbles.
Suppose the joint probability density function of X and Y is uniform in the plane square with corners (0,0), (0,3), (3,0) and (3,3). Find the probability of X > 1 or Y > 1. Find the probability of X + Y
Develop the estimated regression equation for data and plot the residuals against ". Does the residual plot support the assumptions about e? Explain.
Conduct a two-sample test of means. A study by a bank compared the average savings of customers who were depositors for three years or less with those who had been depositors for more than three years.
Graph these data to see whether a linear equation might describe the relationship between the group's television shows and guitar sales and use the least-squares regression method to derive a forecasting equation.
Calculate using excel analysis tools the significance of the difference between the proportion of men and women who support gun control with 74 men oppose.
the u.s. bureau of labor statistics reports that of persons who usually work full time the average number of hours
Find a 99.9% confidence interval for the mean weight of all bumblebee bats at the following confidence levels (two places after decimal):(______, ______)
Xr17-02 Pat Statsdud, a student ranking near the bottom of the statistics class, decided that a certain amount of studying could actually improve final grades.
How much does the low temperature vary on this date? In other words calculate the variance and standard deviation?
If the standard deviation in the above-described scenario had been, how would the results of the hypothesis test change?
Investors use probabilities to decide among several potential investments and calculate potential returns, or losses. An investor has the possibility to invest $2 million in three different schemes.
What is the porbability that less than 20 programmers have had experience in computer programming before being hired.
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