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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
- Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheoryLet f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; isLet X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.
- Suppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.If X is a continuous random variable find the CDF and density of the function y = x/3The time it takes to repair a personal computer is a continuous random variable whose density function, in hours, is given by (See picture) The cost of the repair depends on the time it takes and is equal to 40+30√X when the time is X. Compute the expected time and expected cost to repair a personal computer.