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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?
Other Measures of Dispersion In this section, we look at relatively less used measures of dispersion like fractiles, deciles, percentiles, quartiles, interquartile range and f
entropy test to measure interaction between enviornmental factors and genes
1. Assume the random vector (Trunk Space, Length, Turning diameter) of Japanese car is normally distributed and the unbiased estimators for its mean and variance are the truth. For
Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by
1. For each of the following variables: major, graduate GPA, and height: a. Determine whether the variable is categorical or numerical. b. If the variable is numerical, deter
To study the physical fitness of a sample of 28 people, the data below was collected representing the number of sit-ups that a person could do in one minute. 10 12
TYPE I AND II Errors If a statistical hypothesis is tested, we may get the following four possible cases: The null hypothesis is true and it is accepted; The
These techniques are applied when the rows and the columns of the data table represent the same units and when the measure is a disiance or a similarity. The goal of the analysis i
Consider the following linear regression model: a) What does y and x 1 , x 2 , . . . . x k represent? b) What does β o , β 1 , β 2 , . . . . β k represent?
Median Median is a position average. It is the value of middle item of a variable when the items are arranged according to their values either in ascending or descending order.
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