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An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- 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 19.02arrow_forward9. Let X and Y be independent exponentially distributed RVs with parameters A and B, respectively. Use the MGF approach to find the CDF and the PDF of Z = X+Y. E [e=²(*^_^₂)] = E [e³*] E[e³r] *M(s) XAY = M₁ (3) My (1) = (-_^) ( P-²) =arrow_forwardDetermine the uncertainties in x2 and y2 using the rule for propagating uncertainties when multiplying two numbers. x=80, y=60, ∆x= ∆y=5.arrow_forward
- Suppose X is a random variable with the cdf Fy(x) = 1-(1+x²) x>0, c>0, Y>0 Derive the pdf of the inverse of X, Y=1/x²arrow_forwardLet X, and X; be independent exponential random variables having pdfs f, (x) = e, x > 0 and fr,(x2) = e"", I3 > 0. Given that Y, = X,/X and Y, = X, + X2. a. Find the joint pdf of Y, and Y2 b. Find the marginal pdf of Y1.arrow_forward7.2 dt 7.3x csax dx. (Integration by parts)arrow_forward
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