2. Let X and Y have the joint density (Cx²y if 0 < x < y < 4 f(x) = %3D otherwise a) Find the value of C b) What is the covariance between X and Y?

Q: Q 14

A: Given joint Density function is

Q: Let X and Y have the following joint density: S 1, 0<x<1,0 < y < 1, 0, otherwise. fx,y(x, y) = Give…

A:

Q: Let X and Y have joint density fx,y(x, y) = (6 - x - y) I(0,2)(x) I(2,4) (y). a. Find Var[Y| X = x].…

A: The joint distribution of X and Y is as follows: fX,Y(x,y)=18(6-x-y); 0&lt;x&lt;2, 2&lt;y&lt;4 The…

Q: 4. Given joint density f(x, y) = 1/y, 0 < x < y < 1, compute a) g(x) and h (y), b) P(X <= 1/4 , Y <=…

A: Given joint density function is: fx,y=1y; 0&lt;x&lt;y&lt;1 a). The g(x) and h(y):…

Q: Let X and Y be independent and exponential with parameter lambda. Show that the density of X…

A: Given that X and Y be independent and exponential random variables with parameter lambda.

Q: Let X and Y have the joint density function 2, 0<x<y; 0<y<1, f(x,y)= %3D 0, Otherwise. Then the…

A:

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: Suppose X has density, Find EX 2x for 0≤x≤1 f(x)= 2 Lo otherwise WIN 3

A: Solution

Q: Suppose the joint density function of X and Y is defined as, f(x.y) 2x. 0SIS1, 0sys1 %3D Calculate…

A: Given: fx,y=2x    0≤x≤1, 0≤y≤1

Q: 3

A: It is given that the variables X and Y are independent.

Q: Assuming that X and Y have joint distribution f (x, y) = cx for -x < y < x, 0 < x < 1, and f(x, y) =…

A:

Q: Find the marginal densities of X and Y using the joint density fxy(x, y) = 2u(x)u(y) exp = 2u(x)u(y)…

A:

Q: 9

A: 7.42 From the given information, the joint density function for X and Y is,

Q: Suppose that X has density fx (x) = * for 0 < x < 3 (and fx (x) = 0 otherwise). and suppose that the…

A:

Q: Let X and Y have the joint density function 6x y, 0<x<1,0<y<1, (0, f(x.y)= Otherwise.

A:

Q: Suppose X has density, find EX* f(x) = Lo 2x for 0≤x≤1 otherwise O 1/2 O 3/4 O 2/3 Does not exist

A:

Q: Let G(x,y) and H(x,y) be bivariate cdfs. Is F(x,y) = λG(x,y) + (1 −λ)H(x,y) a cdf (0 ≤λ ≤1)? Answer…

A:

Q: - Let x and y have the joint density f(x, y) = {* + cy if1<x<2;0sys1 elsewhere mere c is a constant

A: The value of c is obtained below: ∫x=12∫y=01f(x,y)dxdy=1∫x=12∫y=01(x+cy)dxdy=1∫x=12xy+cy2201dx=1…

Q: Let X and Y have the joint density as follows: f(x,y) = (x + y)², 0<x< 1, 0 <y<1 f(x,y) = 0…

A: Obtain the marginal density function of X. The marginal density function of X is obtained below:…

Q: (a) Let Z = vX. Show that the density function of Z is given by %3| (-). fz(z) = 2a exp z > 0.

A:

Q: 1. Show that the density function f(x; a, B) has a relative maximum at x = a-1 a+B-2'

A:

Q: Let (X,Y) ~ Dirichlet(1,1, 1). That is, the joint density of X, Y is S2 if 0 < x < 1, 0 < y < 1, 0 <…

A: E1X+Y=∫01∫011x+yfx,ydx dy=∫01∫012x+ydx…

Q: 1) Let f(x,y) = 6x,0 < x < y<1 and 0 elsewhere. Find a) The marginal density of X and Y

A: The provided information is  f(x,y)=6x    0&lt;x&lt;y&lt;1   and 0 otherwise Therefore  a. The…

Q: 1. Hand in: Let f(x, y) = 6y(1 – y), function. Find E(X|Y = y) 0 <x<y<1 and zero eswhere be a valid…

A: A joint probability density function for the continuous random variables X and Y is the…

Q: If f (x) = c (9 – x²) for 0 < x < 3 is a density then c is equal to

A:

Q: Let and Y have the joint density function 2, 0<x<1; 0 <y<x, f(x,y)= 0, Otherwise. Calculate E(XY).

A:

Q: Assuming that X and Y have joint distribution ƒ (x,y) = cx for –x < y < x, 0 < x < 1, and f(x, y) =…

A: Suppose that X and Y have joint probability distribution f(x,y)=cx for -x&lt;y&lt;x,0&lt;x&lt;1…

Q: 7.* Give the candidates to local extrema (maximum or minimum) of f(r, y, z) = 2z – y – r under the…

A: The solution to the given question is as follows.

Q: Let X and Y have joint density fx,Y(x, y) (a) Find Var[Y|X = x]. (b) Show that E[X] = E{E[Y|X]}.

A: Thanks for giving opportunity to serve for bartleby students,   Hey, There ! Thank you for posting…

Q: Suppose there is a random vector (X, Y) of density f(x, y): 10<x<3y³€ • Find E(Y|X) • Find…

A:

Q: For variables X and Y which have joint density function given by: cy, 0<x< y < 2 0, fx,y(x, y) =…

A: Given f(x,y)=12xy,0≤x≤y≤2 (a) f(y)=∫0yf(x,y)dx      =∫0y12xydx     =12yx220y     =14y3…

Q: Suppose, we have the joint density of X and Y as fxy(x, y) c(x² + y²); 0 < x < 1,0 < y < 1 0,…

A: a) we know that the sum of all the probabilities is one. so,…

Q: If X has density ƒ (x) = (x+1)² for | x| < 1 then E (X) =; and Var (X) =

A: if X has density f(x)=38(x+1)2 for x&lt;1 then  E(X)=12 Find Var(X)=?

Q: 2 Let fxy (x, y ) = x + y for 0S x< 1, 0 < y <1 = 0 otherwise %3D Find the conditional density of…

A:

Q: Let X and Y have the joint density function 0<x<1; 0<y<x, 2, f(x,y)= 0, Otherwise. Calculate E(XY).

A:

Q: Find M,, M,, and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.…

A: Momentum and centre of Mass:

Q: no clue how do this,

A: The parametric equation of the of wire:

Q: 4. Consider the density function 0.5 <x < 2.5 f(x) = }kvx, 0, %3D elsewhere. a) Evaluate k. b) Find…

A: a) The total area under the probability density function is one.…

Q: 1. Suppose that D is a region with area A, on the xy plane and that f (x, y) is a continuous…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Suppose that X and Y have joint density function fx.y (x, y) = x² + xy for 0 < x < 1, 0 < y < 2 (and…

A:

Q: Suppose that X has density fx (x) = for 0 < x < 3 (and fx (x) = 0 otherwise). and suppose that the…

A:

Q: 9

A: 7.52From the given information, the joint density function for X and Y is,

Q: Let X and Y be jointly continuous with density fxy (x, y) = 2xy for 0 < 2y < x < 2. Then E (XY) is…

A:

Q: Suppose X and Y have joint density given by, 1, 0<*<1,0<y<1 f(2, y) = ( 0, otherwise 1. Prove that…

A: Consider the case of two random variables, X and Y, both of which have finite means and variances.…

Q: Find M M and (x, y) for the lamina of uniform density p bounded by the graphs of the equations. x= y…

A: Firstly to know the limits of the integral we need to solve y2-y-42=0. By applying the direct…

Q: If R(t) = ae-bir. Find the spectral density func- tion, where a and b are constants.

A:

Q: 6. The joint density of X and Y is given by I(x, y) : /y if 0 <z< 0, 0 <y< ∞ otherwise. Compute…

A: Given, f(x,y)=e-x/y-yy  if 0&lt;x&lt;∞,0&lt;y&lt;∞0                 otherwise

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.