An engineer is studying early morning traffic patterns at a particular intersection. The observation period begins at 5:30 AM. Let X denote the time of arrival of first vehicle from north-south direction. Let Y denote the first arrival time from east- west direction. Time is measured in fraction of an hour after 5:30 AM. Assume the density for (X,Y) is given by fx,r(x, y) = { 0 0.25).

Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

Q: If f(x, y, z) = excosy + z, show that fxx + fyy + fzz = 0

A:

Q: Let f(x.y) = ry. a. Sketch/describe the domain of g Domain = { (x,y)]yz0} b. Sketch a contour map…

A:

Q: Use differentials to estimate the change in f (x, y, z) = x² In(5yz + 1) as (x, y, z) changes from…

A:

Q: f(z) = ze-32*. Please determine the average value of f over the interval [1, 3].

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: of Let f(x,y) = xy° +7. Evaluate at (x,y) = (-7,1) and interpret the results. ду -

A: In this question we have find δfδy at (x, y)=(-7, 1)

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

Q: Let f(x, y, z) = xyz Find the direction in which the function increase most rapidly at the point…

A: Given: fx,y,z=xy2z3 The gradient of a function if given by ∇f(x,y,z) =∂f∂x,∂f∂y,∂f∂z.

Q: Let X ~ Uniform(-1,1) and Y = X² , find the CDF and PDF.

A: Use the following definitions, to obtain the solution. The cumulative distribution function of a…

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>0

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.