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Suppose X is a binomial random variable with parameters n and p. (i.e., there are n trials). Suppose Y is a binomial random variable with parameters n and q. Suppose also that 0 p < q 1. True or false?: P(X k) P(Y k), for any k. If true, provide a proof. If not true, provide a counterexample. (Hint: if you're having trouble, simplify by considering small n.)
A formula is derived for the n-th derivative of a function that is a product of two other functions, f(x)=u(x).v(x). This formula is used to write down the n-th derivative of f(x) = e^x/(1 − x).
you have 240 feet of fencing to form two adjacent rectangular corrals. each coral has an area of 1000 square feet, find the possible dimensions of each corral.
a company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 60ft^3. what dimensions yield the minimum surface area?
The region in the first quadrant bounded by the graphs of y = x and is rotated around the line y = x. Find (a) the centroid of the region and
Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.
imagine you are a manager at a major bottling company. customers have begun to complain that the bottles of the brand
Probabilities, A survey of MBA students obtained the following data on "student's first reason for application to the school in which they matriculated".
Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer.
Calculate the value the test statistic
Probability: High Risk Apartments. In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants.
Find the center of mass of the lamina bounded by y = x^2 and y=2x and the density is ?(x,y) = xy.
Analyze the stability of the fixed points of linear differential systems. Provide several explicit examples, with graphical illustrations
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