Suppose X and Y have joint pdf f(x, y) = {ax²y (ax²y, x² ≤ y ≤ 1 0, otherwise

Q: 4) y = e3r* dy A) 12x dx B) dy 3* . 12x³ = e dx dy 3x e C) dx D) dy „3x* - 1 . 12x = e dx

A: Given below the detailed solution

Q: 'y' and evaluate each at the given point. ху f(x, y) = - (2, -2) %3D x - y f,(x, y) = %3D ,(x, y) =…

A:

Q: Is f(x)= Vx + 1 continuous at x == -1

A: Draw the graph and check continuty with help of limit of function.

Q: 14. Poker hand consist of five cards Find the total number of possibilities but hot poker hand. B.…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Let f(x, y)= x'y+2x² and find f.(1,2) and f,(1,2) %3D 3x- y 1.

A: The given function is: f(x,y)=x2y+2x23x-y

Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: 2) Find a value of c for which f (x) is a pdf on the f(x) = cx + x², [0. 1]

A: Introduction ∫-∞∞fxdx=1 The total area under the curve fx of pdf is 1.

Q: Suppose that X and Y have joint pdf (8xy 0< y<x<1 f(x, y)=- otherwise Find the joint CDF. Find fy…

A: Given:

Q: Use the second-derivative test to show that the function f(x, y) = x²eY – y²e* has a saddle point at…

A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: 2. k) Show that fe2) = function is analytic %3D t'+s for Rez 70.

A: Calculate the limit: lim∆z→0fz+∆z-fz∆z=lim∆z→0∫0∞e-tz+∆zt2+1dt-∫0∞e-tzt2+1dt∆z…

Q: Let f(x,y) = cx2y, x2<=y<=1, -1<=x<=1 be the pdf of X and Y. Find the value of c that makes this a…

A:

Q: Is the function F (x) = L", e“ dt concave (concave down) or convex (concave up) for x<0?

A: To solve the following problem

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

A:

Q: f(x, y, z) = e2* +e3y + e4=

A:

Q: Find f'cx?, f"cxx) wheve fcK) = xe -2 Jc %3D

A:

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: (3) Determine the values of a for which x4 + y* , if(x, y) # (0, 0), (x² + y?)ª f(x, y) = ,if(x, y)…

A: solution.

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: et f(x,y)= x^2-xy+y^2-y   what are the min and max values of Du f(1,-1)?

A: Given :  f(x,y) = x2-xy+y²-y  To find :  Maximum and minimum values of directional derivative at…

Q: a red coin as a 1 on one side and a 3 on the other. a blue coin has a 0 and 1. let X represent the…

A: Given Red coin→ 1,3 Blue coin→ 0,1 X→ Total of both coins Y→ No. flipped on the blue coin

Q: Let a differentiable function z = f(h²(x² + y3), 2łn(x +y)) satisfying the condition f(4,0) 1 be…

A: We need to find the partial derivative of z with respect to x for the given function.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

A:

Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Let X ~ Exp(λ). Find F(X) and E(X).

A: Let X ~ Exp(λ)The probability density function of X is fx(x)=e-λx   ;x&gt;0

Q: 6. If f(x,y) = 2 x>0; y>0; x+y<1 Show the conditional pdf of Y given x is uniform.

A:

Q: Find all point(s) of inflection, if any, of the graph of the function f(x) =x* – 2x'. с. (-1, 3) а.…

A:

Q: (a) Compute P[(X = (1/2)]

A: