for query regarding above comment
3. Work out Example 4.18 in the lecture notes by using the CDF method. Example 4.18...
Please do #16 AND #17 parts in clear legible handwriting.
Explain answers in clear work and detail. The final answers are
provided for each part/problem to use as a reference to check work.
If both problems are not completely done, I WILL mark you down and
give a thumbs down. Thank you
16) Sketch the region of integration and evaluate by changing to eV2x-x 1 dy dx 2-In(1+ 2) polar coordinates. 17) Let E be the region above the sphere...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
Reserve Problems Chapter 5 Section 4 Problem 3 Suppose that X and Y are independent continuous random variables. Show that oxy o If X and Y are independant, then fxy (x, y) = – fx (x) - and the range of (X, Y) is rectangular. Therefore, fyy) / xyfx (x) dx E(X) fy(x) [fy(x) dx E(Y) Hence, Oxy = 0 Fan- | | C = 15 If X and Y are independant, then fxx (x, y) = fx (x) +fy...
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integrationRin Figure 3.(b) By completing the
limits and integrand, set up (without evaluating) the integral in
polar coordinates.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
calculus 3.
Answer all of the following, I will rate your work if you do
so.
Evaluate the double integral || xy2da, where Ris the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. Evaluate the iterated integral. 1 ya x-y xy dz dx dy xy dz dx dy 0 V The figure below shows the solid region Ein the first octant bounded by the...
Please Answer the Following Questions (SHOW ALL WORK)
1.
2.
3.
4.
Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
6. (4 pts) Consider the double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.
2 1 2 X -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 2-y2 (2? + y) dA= (32 + y) dx dy + (x2 + y) dx dy. 2-y? (a) ketch the region of integration R in Figure 3. (b) By completing...
10) Calculate the integral zdac dy dz where D is bounded by the planes x = - 0, y = 0, z = 0, z = 1, and the cylinder x2 + y2 = 1 with x > 0 and y> 0. 11) Let y be the boundary of the rectangle with sides x = 1, y = 2, x = 3 and y = 3. Use Green's theorem to evaluate the following integral 2y + sina 1+2 1 +...
3. Let X.. U(-1,1) for i € {1, 2, 3). (a) Write down the expected value and variance of X,. Sketch the pdf fx. [3] (b) Let Y = X1 + X2. Compute the pdf fy of Y and sketch it. Using fy, or otherwise, compute the expected value and variance of Y. (7) (c) Let Z = X1 + X2 + X3 = Y + X3. Using exactly the same technique that you used in part (b), it can...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...