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Among the students doing a given course, there are four boys enrolled in the ordinary version of the course, six girls enrolled in the ordinary version of the course,and six boys enrolled in the higher version of the course. How many girls must be enrolled in the higher version of the course if sex and version of the course are to be independent when a student is selected at random?
A plays tennis against B. During a given game, the score reaches deuce. Each player then needs to score two more points than the other to win the game. Assuming that each point is independently won by A with probability p, what is the probability they will have to play a total of 2n points to end the game? What is the probability that A will win the game?
Suppose the random variable X is continuous and has the distribution F(x). Consider another random variable Y de?ned by Y = F(X). Find the distribution of Y .
In a sequence of independent identical trials with two possible outcomes on each trial, success or failure, and with P(success) = p, what is the probability that exactly x trials will occur before the rth success?
Flow Chart for Confidence Interval We can now prepare a flow chart for estimating a confidence interval for μ, the population parameter. Figure
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The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the to
Factor analysis (FA) explains variability among observed random variables in terms of fewer unobserved random variables called factors. The observed variables are expressed in
Scenario: Many of the years 5 and year 6 learners' at Woodlands Park School were excited about being chosen for the cross-country team. Every day, they were able to run laps of t
Systematic Random Sampling This method is generally used in such cases where a complete list of the population is available from which sample has to be selected. Under this
A manufacturer has received complaints that aging production equipment is forcing workers to work overtime in order to meet production quotas. Historically, the average hours worke
Exercise: (Binomial and Continuous Model.) Consider a binomial model of a risky asset with the parameters r = 0:06, u = 0:059, d = 0:0562, S0 = 100, T = 1, 4t = 1=12. Note that u
In the case of permanent magnet DC motor whose stator consists of a permanent magnet we can take the field current to be constant (i.e. a constant magnetic field) and it can be sho
For each of the following scenarios, explain how graph theory could be used to model the problem described and what a solution to the problem corresponds to in your graph model.
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