Real Analysis: Multivariate Probability Distributions
Please see the attached file for the fully formatted problems. Multivariate Probability Distributions f(y1,y2) = 3y1, 0<y2<y1<1 f(y1,y2) = 0, elsewhere Find P(0<y1<0.5, 0.25<y2)
Please see the attached file for the fully formatted problems. Multivariate Probability Distributions f(y1,y2) = 3y1, 0<y2<y1<1 f(y1,y2) = 0, elsewhere Find P(0<y1<0.5, 0.25<y2)
Please see the attached file for the fully formatted problems. Show that is a representation of the Dirac S-function. Discussion: Let and let f(x) be a function which is piecewise continuous on [?a, a], in particular, (Dirac delta function) one must show that One way of doing this is to follow the approach u
Please see the attached file for the fully formatted problems. Suppose that f(x + 2pi) = f(x) is an integrable functionof period 2pi. Show that S f(x) dx 2pi + a ---> a = S f(x) dx 2pi ----> 0 where a is any real number.
Int sqrt{1+x^2}/x dx
Evaluate limit of [x] as x approaches 2, where [x] is the greatest integral value less than or equal to x.
Hello! I'm having trouble using Trigonometric Substitution to find the anti-derivative of non-simple integrands. For details on my situation, please consult my missive, which I've included as an attachment in MS Word '95 (WordPad compatible) and Adobe PDF (ver 3+) files. (The files contain identical information; if you can re
Please see the attachment for the full question. I require full, detailed, step by step workings for all sections of this problem Coursework 2 Question 2 a) For the curve with the equation y = x^3 + 3x^2 - 2 i) Find the position and nature of any stationary points. ii) Make up tables of signs for y, y' and y''. Us
( f ^n_r means that n is on the top of the f and r is on the bottom) Evaluate the iterated integral: f ^(pi/2)_0 f ^(pi/2)_0 cos x sin y dy dx f: is the integral symbol
Question: Solve by triple integration in cylindrical coordinates. Assume that each solid has unit density unless another density function is specified: Find the volume of the region bounded above by the spherical surface x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 + y^2.
Compute the value of the triple integral   _T f(x, y, z) dV: f(x, y, z) = xyz; T lies below the surface z = 1 - x^2 and above the rectangle -1*x*1, 0*y*2 in the xy-plane. : is the integral symbol
(  ^n_r means that n is on the top of the  and r is on the bottom) Evaluate the given integral by first converting to polar coordinates:  ^1_0  ^(square root of 1 - x^2)_0 (1/(square root of 4 - x^2 - y^2)) dy dx : is the integral symbol
Please show all work; don't explain each step. Please DON'T submit back as an attachment.Thank you. (  ^n_r means that n is on the top of the  and r is on the bottom) Sketch the region of integration, reverse the order of integration, and evaluate the resulting integral:  ^1_0  ^1_y
Evaluate the iterated integral: The integral from 2 to 1 * the integral from 3 to 1 * (x/y + y/x) dy dx
Find all the roots of x^2 + 3x - 4 in Z (integers) AND Z6 (integers modulo 6) AND Z4 (integers modulo 4)
The region bounded by the curve and the lines and is revolved around the x-axis to form a solid S. The volume of S by the method of washers is given by the integral . Find the volume using the method of cylindrical shells. Please show the complete solution (particularly how to find the cross-sectional area), including al
Please see the attached file for full problem description. Can somebody help me to evaluate the following integral,
a) Take the region bounded by y = cos x and y = 1 - x for 0 ≤ x ≤ and rotate about the line x = . Set up the integral which calculates the volume of rotation (using one variable only). b) Complete the integration without using integral formulas or calculator estimates. (Please show work on this so that I can see
Show that there are exactly four distinct sets of integers which satisfy the attached equations:
Given dy/dx= -xy/(ln y), where y>0 find the general solution of the differential equation What solution satisfies the condition that y=e^2 when x=0... express in y=f(x) Why is x=2 not in the domain found from that?
20) If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true? a) f(a) = 7 b) f is differentiable at x=a. c) f is differentiable for all real numbers. d) f is increasing for x>0. e) f is increasing for all real differentiable ans is B. Explain
Evaluate the integral in the attached file "Arc Length.doc" for arc length (L). The intent is to solve for a numerical answer and the values for a, b, and t are all constant.
Can you show me the solution to this integral? See attached file for full problem description.
Can you please show all the working to solve the attached integral? See the attached file.
Please see the attached file for full problem description. --- Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x+y)sin(x-2y). over the square region with vertices at (0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables). Solution. Letting
Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at O(0,0) P(1,-2) Q(3,-1) & R(2,1) (My notes from class-uses substitution, change of variables)
Can anyone show me the working between the integral in the enclosed file & the answer of A = 4/3 First let's sketch the graph for 0≤t≤2п: Ok, so one loop is the half of this, i.e. 0≤t≤п: Now we have: where x=f(t) and y=g(t). Then we have: or: A=4/3
Can anyone please show me how to solve these double integrals, with a step by step approach. I know the answer is 63 - but Ive tried so many times & I don't know where I'm going wrong. upper limits are 1&y=2 x+4y^2 dydx + lower limits are -2&y=-x upper limits are 4 & y=2 x+4y^2 dydx lower limits ar
Use a transformation to evaluate the double integral of f(x,y) given by f(x,y)=cos(2x-y)sin(x+2y) over the square region with vertices at (0,0) (1,-2) (3,-1) & (2,1) (My notes from class-uses substitution, change of variables) I have let u=(2x-y) & v=(x+2y) using substitution (change of variables)
In some populations, the amount of births is directly proportional to the population at any given point in time and the amount of deaths is directly proportional to the square of the population at any given point in time. 1. Write an equation that models the change in a population that fits the above description. Make sure t
Please see the attached file for full problem description.