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Let x1, x2 denote the variables for the two-dimensional data in Exercise 1. Find a new variable y1 of the form y1 = c1x1 + c2x2, with c21 + c22 = 1, such that y1 has maximum possible variance over the given data. How much of the variance in the data is explained by y1?
Exercise 1
Convert the matrix of observations to mean deviation form, and construct the sample covariance matrix.
If BCD and EFGH are rectangles with AB=10cm,BC=7cm,EF=7cm and FG=4cm,all figures accurate to the nearest cm. Find (a)the largest and (b)the smallest possible values of the shaded area.
If you deposit $5000 into an account paying 8.25% annual interest compounded semiannually, how long until there is $9350 in the account?
Let (X,d) be a compact metric space, and let Con(X) denote the set of contraction maps on X. We shall define the distance between two maps f,g which belongs to Con(X) as follows:
The width is increased by 4 while the length is unchanged. Using a as the variable, express the change in area in terms of a.
the probability that a smoker will quit smoking increases with the smoker eductional level. the probabilty (expressed as a percent ) that a smoker with x years of education will quit is approximately
A bowl is shaped like a hemisphere with diameter 36 cm. A ball with diameter 4 cm is placed in the bowl and water is poured into the bowl to a depth of h centimeters. Find the volume V of water in the bowl. Consider two cases: one in which the bal..
A pollster wants to determine the difference between the proportions of high-income voters and low-income voters who support a decrease in the capital gains tax. If the answer must be known to within 0.2 at the 95% confidence level and the sample ..
Two tourists with a surveying tool want to measure the distance from their hotel to the Washington Monument and to the Lincoln Memorial. From the top of the Washington Monument, they find that the angle hotel-Washington Monument-Lincoln Memorial is65..
Answer the following: What is the bottom line for the preschool's budget? The payroll is run every two weeks. What is the usual paycheck for each of the three employees
Consider the area A of the triangle with vertices [a1 a2]^T [b1 b2]^T [c1 c2]^T. Express A in terms of.
define the term linear inequality, then explain what it means to solve a linear inequality. Explain how the solution to the inequality 2x-5
A boat's crew rowed 9 miles downstream, with the current, in 1.5 hours. The return trip upstream, against the current, covered the same distance, but took 3 hours. Find the crew's rowing rate in still water and the rate of the current.
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