Let Y be continuous defined on (0, 1) with pdf given by f(y) = 2(1-y), 0 0.67
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- Differentiate. f(w) = w / [w + (d/w)]Let X X,"ExpiB).S(x) = Be "1>0.IM, = Find the pdf of Y = E,X, (a) r(n.ß) (b)r(1,B) (e )r(n, nB) (d) exp(nB) (e) NoneSuppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices (- O), (0,1). (This means their joint PDF is a constant). Find the joint PDF of X and Y, call if f (x,y). Find fy (y)
- Let y be a function of x and suppose *=In(x--y-). what is the correct result for the derivative of y with respect to x? dy 2x dx 2y – x24 -x²+y2 dy 2x В dx x²– y²+ 2y dy x2- y2– 2x dx 2y dy 2x – x²+y² D dx 2y ||Let X have cdf Fx(x) = 1- (1+x)^-A, x,a > 0. Determine the pdf and cdf of Y = CXDetermine if the function is continuous at point (0,0): _x³y³cos(x³+y³) F (x, y) (x2+y²)2
- Determine if the function is continuous at point (0,0): F(x, y)= F(x, y)=**y°cos(x²+y³) (x²+y²)²Assume the second derivatives of ƒ are continuous throughout the xy-plane and ƒx(0, 0) = ƒy(0, 0) = 0. Use the given information and the Second Derivative Test to determine whether ƒ has a local minimum, a local maximum, or a saddle point at (0, 0), or state that the test is inconclusive. ƒxx(0, 0) = -6, ƒyy(0, 0) = -3, and ƒxy(0, 0) = 4Let esinx rcosx f(t) dt and f is a continuous function, determine the value of f