Suppose X and Y have the joint pdf f(x,y) = c(1.57-x-y), x+yo, y> 0 a) Find the value of c so that f (x, y) is a proper pdf? b) find E(X,Y) b) Calculate E (XY)

Q: j Find y as a function of æ if a?y" – 9xy' + 25y = xº, (1) — 2, У(1) — -5. y =

A:

Q: dx 2x² + 5x +1

A: The formula for the integration is given by  ∫dtt2-a2=12alnt-at+a+C.

Q: Consider a function f: R? → R°, the derivative of f isa O 3 x 3 matrix O 3 x 2 matrix O 2 x 3 matrix…

A:

Q: f(x, y) = ln(-6x – 4y), (5,6), A=6i + 8j 14 17 A) 135 135 B) C)/17 D) 11 135

A: Duf=∇f·uu

Q: For each of the following functions, Find c so that the function is a PDF. a) (cx² + x) I[0,1](×).…

A: The value of C, so that the given functions are a pdf.

Q: Determine the value of b to make the PDF below valid given that a=1and c=2. Note that the PDF…

A: #Given: pdf of exponential distribution  f(x)=b*e^-c(x-a)  if a=1 , c=2  then to find value of a ?

Q: Consider the function f(t, p) 3 (pе' +1—р)". a. Find an expression for f(t, p) and evaluate that…

A: Given that:f(t, p)=(pet+1-p)n

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f.(x,y) =.

A: Note: We are allowed to answer only first three parts of the multiple questions asked. Please post…

Q: (3, 4, 3) Let v = Calculate: vxi=( vxj=( v x k = ( A F ->

A:

Q: (In æ)" Find y'. Let y = e" + 2

A: Explanation of the solution is given below...

Q: Let v = (2, (2, 3, 2) 3,

A:

Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

Q: Differentiate the function. = In({ (4t+ 1)³ (4t-1)5 F'(t) = F(t) = In

A: The derivative of the function in the division form is given by the quotient rule which is given by-…

Q: Suppose X and Y are the coordinates of a randomly sampled point in the triangle with vertices…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subparts.

Q: Exercise 10. Find the derivative d 7x (* + 2) dt dx

A:

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

A:

Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p…

A: Step 1:Use Ideal gas Law;PV=nRTInternal energy can be related to ideal gas…

Q: 4. Given a function, fix), such that f(x)dx = 10, calculate: a) - r(«)dx b) S rx - 2)dx d) Stsx) +…

A:

Q: A) B) dx₁ dt dx₂ dt dx₁ dt dx2 dt dx₁ dt dx₂ Wh = x₁ + 2x₂ + 2x₁.x2 = x₁ + x₂-X1X2 is stable or…

A: Given :           A) dx1dt=x1+2x2+2x1x2    dx2dt=-x1+x2-2x1x2           B) dx1dt=-x1+x2+x12…

Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

A: Given function is, fx,y=4y2x3+ex2y To find fxy(x,y) Find fxx,y partially differentiating the given…

Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

A:

Q: Find p, q if f,º f(x) dx – L f(x)dx = [" 5(x) dx. (Give your answers as whole or exact numbers.) p =

A:

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

A: