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EBK AN INTRODUCTION TO MATHEMATICAL STA
- Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial derivative fx, fy, and fz of (x + yw )2 – ez – 2 = 0 and f ( x , y, z ) = 2xyz + tan x + y sin z Make the solution detailed and clear IN A PAPER.arrow_forwardState TWO (2) dissimilarities between Green’s and Stokes’ theorems.arrow_forwardSuppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane, and let My be the plate’s momentabout the y-axis. Show that the plate’s moment about the linex = b is My - bδA if the plate lies to the right of the line, andarrow_forward
- Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev, where a=6, b=5. Show all necessary stepsarrow_forwardFind all the second-order partial derivatives of the functions in Exer-cise. 46. s(x, y) = tan^-1( y/x)arrow_forwardLet X,Y have joint pdffX,Y (x,y) = x + y,for 0 < x,y < 1i) Find the marginal pdfs of X,Yii) Find the conditional pdf of Y given X = x.arrow_forward
- Consider the unit cirlce in the plane; that is, the set of all points within a distanceof 1 of the origin: A= {(x, y) : x^2 + y^2 ≤ 1}.Suppose we choose a point (X, Y ) uniformly at random from S. What is the pdf for thedistance B = √X^2 + Y ^2 from the origin to this point? Hint given: What is the cdf of B?arrow_forwardLet Y be a uniform r.v. on the interval (0,1). find E[Y^k] using method of MGF. (Moment Generated Function Be detail. Thanksarrow_forwardcalculate the first moment of the beta function using intergration given that alpha =1 and beta = 4arrow_forward
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