1. Suppose X and Y are jointly distributed with pdf fx,y (x, y), where fx,y(x, y) = — e-(x−y)² e-x². TT Note that fx (x) = f e-(x-y)² e-x² dy. TT a. By making the substitution t = y - x, simplify the expression for fx (x) by 1 e-((t-μ)²/(20²)) evaluating the integral above. You may use the fact that is the probability density for a normal random variable with mean μ and variance o2, so that 8 Love e-((t-μ)²/(20²)) dt = 1 1 V2πσ2 for any values μ and o b. Find f(y|X = x) (y). (Note that your answer will depend on both x and y. This is because for each value of x, there is a different marginal distribution for Y which is a function of y.) c. Find E[Y|X = x]. (Hint: for part b., you should have gotten a normal distribution. Note your answer will be a function of x only.) d. Find Var E[YIX]]. (Hint: In your answer for c., replace x with X.)

Q: A table of values for f, g, f', and g'is given. f(x) g(x) 3 2 x 1 2 3 ليا 1 7 8 2 (a) If h(x) =…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Suppose that f(x) Evaluate each of the following: f'(3) = %3D f'(-1) =

A: Given function is : fx=3x9 The given function can be written as : fx=3x-9

Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

A:

Q: Let r(æ) = f(g(h(x))), where h(1) = 3, g(3) = 2, h'(1) = 9, g/ (3) = –2, and f'(2) = 5. Find " (1).…

A:

Q: A table of values for f, g, f', and g' is given. g(x) 2 8 2 Xx 1 2 3 f(x) 3 1 7 (a) If h(x) =…

A:

Q: Let f(1) = 1, g(1) = -3,h(1) = 2, f'(1) = -1,g'(1) = 2, and h'(1 d f(x) g(x) dx h(x) Find when x =…

A: Please refer to the image below

Q: Let S(x) = 4x$ (x' – 6). Evaluate the following specific values of f: (A)(2) = (B) (4) =

A: The objective of the question is evaluate the values.

Q: Find a function y(æ) such that byy' = x and y(6) = 5. y =

A: y' = dy/dx y(6) = 5 means at x=6 => y=5

Q: Estimate g(1.2) − g(1) if g'(1) = 4.

A: Given: g'(1)=4 Now, Using the Linear approximation formula:

Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: If F()dt= x*, then f(8) = %3D (A) 32 (B) 0

A: Given: By Euler's formula for integral,              ddx∫0x3f(t)dt=ddx(x4)⇒f(x3)…

Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: Compute the derivative of f(x) = (x² + 3)e7x+5. O (x² +2x+3)e7x+5 O 14xe7x+5 O (7x2 + 14x + 21) e7+5…

A:

Q: If x' x= [(-₁)] and x(0) = [] x what is X(T)?

A: Given: x'=01-10x and x(0)=01. To find: x(π)

Q: fand g are the functions whose graphs are shown, y = f(x) is in black and y=g(x) in red. Define H(x)…

A:

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 2. 4 1 8 7 3 7 7 9 (a)…

A: Solve the function

Q: (x+1)(1-x) 9. y = (x+2)2 10. y = (2x2 - 1)(3x + 2)³

A: Given  y=x+11-xx+22

Q: If h(2) 9 and h'(2) = -4, find %3D %3D d (h(x) dx x = 2

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: If f(x) = (3x – 2)(2x + 3), then a. f(– 2) b. f'( – 2) = c. f''(– 2) d. The values of x for which…

A:

Q: Suppose X and Y are independent variables such that E[X] = 2, E[Y] = 3, E[X^2] = 9 and E[Y^2] = 15.…

A:

Q: F(x) = "(5t - 1) dt %3D

A: We need to find the first derivative of F(x)=∫x2x(5t-1)dt. By Leibniz's integral rule,…

Q: f(x) = ex/³; [1₁3]

A:

Q: Find (f1)'(3) given the following table of values. f(z) f'(z) 3 1

A: The given table is, x fx f'x 2 3 1 This means that, At x=2,   fx=3   and  f'(x)=1. That is,…

Q: 04:- Use the Chain rule to find the derivative ) of z = 3x2 - 2 xy y and If x=x (u, v) = 3u + 2v and…

A: Please refer to the image below.

Q: - If g(x) 1 dt , find g'(2). 4 +t

A: