8. Given the Beta Distributionwherep(x) = B(a,b).ªªa-Calculate the mean and varianceB(a, b) =-xª-¹ (1-x)b-11= √₁² 2²-x-¹(1-x)-¹dx =r(a) I (b)I(a + b)

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Answered: 8. Given the Beta Distribution where…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(d) Does a linear relation exist between the speed at which a ball is hit and the distance the ball travels? The variables speed at which the ball is hit and the distance the ball travels are positively associated because r is positive and the absolute value of the correlation coefficient is greater than the critical value ( ) (Round to three decimal places as needed.)
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11.
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).
5. (a) Establish the formula: nroxdy = n,r,0x, Oy, + n2r20x,Oy, + n,dx,dy, + nzdx,dy2 Where dx, = x - i, dy, = 91 - y, dx, = X2 - X, dy, = y2 - y 5. (b) Find the correlation coefficient of combined sample given that %3D %3! Sample Size Mean of X Var(X) Mean of Y Correlation between X and Y Var(Y) Group 1 n = 100 i, = 80 ox? = 10 y, = 100 o = 15 %3! = 0.6 Group 2 n2 = 150 = 72 Ox = 12 y, = 118 o = 18 2 = 0.4

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8. Given the Beta Distribution where p(x) = Calculate the mean and variance B(a, b) = 1 B(a, b) -r@-1(1−z)-1 = √√₁² 2²- rª-¹ (1-x)b-¹dx = r(a) (b) I(a + b)