Let X~U(2,3) and Y~U(1,3) be independent. Give E(XY). O 5 O 0.5 O None of the options O 2.5 O 4.5

Q: 12. Define def M e-$dWg• s=0 For each t > 0, compute (a) E[M¡]. (b) E[M?]

A: Given  Mt=∫s=0te-s dWs      , where W is a Brownian motion.

Q: 3-If u(x),v(x) and w(x) Find d/dx of (uvw)

A:

Q: =E %3D i=1 j=1 j#i Hence, O A. Yes Y is an unbiased estimator of uy. O B. No, is not an unbiased…

A: Given Y1,Y2,...,Yn be i.i.d Mean =μYVariance=σY2 Y__ is an Unbiased Estimator of μYEY__=μY We know…

Q: If AB = B for some B # 0, then A is inertible.

A:

Q: If f(x) = exp(-x).In(x), then , when x=1, df/dx is 1/e C 2/e O e nonexistent O

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

A:

Q: If the function u = ln (2¹+2²4-7² I-Y O2e^u O e^2u 0 2 O 1/2 O Other: then x + y sy Sx is

A:

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: Let z z'y- zy?, z = e ",y = e", then which of the following is ? 3012 O a. 2e- 2e 24 O b.0 Oc-2e-2e…

A:

Q: Determine E (X) and V (X) f(x,y) 1/3 у -1.0 -2 -0.5 -1 1/6 0.5 1 1/6 1.0 2 1/3 a. None O b. E(X) = 0…

A:

Q: If u = f(x), then ſ dx x++2x²+1 k + C for some constant k . Compute kf(1). x2+1

A: We have to find kf(1) Given that: u=f(x),∫xx4+2x2+1dx=kx2+1+C  for some constant k

Q: X E R, 3y ER: Iny >e* Select one: O True O False

A: The domain of the natural logarithm function "ln" is 0,∞. The range of the natural logarithm…

Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X & Y are independent then we say that…

Q: Let D-{tx.y.2) : 2+y?s2s 1, z2 o}. Evaluate z dv.

A:

Q: Let a e R" and let A = aaT. Show that xT Ax = (a" x)².

A:

Q: f: [o,17 s R. )m =l,2,3, fcx) = 3. otherwise Prove that f t R[O,1]

A: The given function is f: 0,1→Rwhere f(x)=1 if x=1n,n=1,2,3,...0 otherwise

Q: (d) VX € P(N), XCR. (e) In ɛ N, VX e P(N), |X| < n. (f) Vn e Z, 3X c N, |X| = n. (g) 3me Z, Vn € Z,…

A:

Q: The ODE M(z. v) dz + N(z. v) du = 0 is exact if and only if

A:

Q: In SRSWOR show that E(y )= Y

A: ANSWER: For the given data,

Q: 2. Let P: C(0, 1]C(0, 1] be given by Pp "- e. Compute dP(x). Be sure to justify your calculations.

A: Given: The given function is  P:C20,1→0,1 given by pφ=φ''-eφ

Q: Sw 1. Given w = xysin( z?), x =s-t, y = s2, z = t2. Use the Chain Rule to find St

A:

Q: solve the following P.D.E: azu ди + u at əx2 u(0, t) = u(1,t) = 0 (1, 0<x<1/2 10,1/2 < x <1 u(x, 0)…

A: Let the solution of the equation be ux,t=XxTt. On differentiating, we get uxx=X''xTt and ut=XxT't.…

Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

A:

Q: Suppose that X and Y are unknowns with E ( X ) =12 and E ( Y ) =20.  If E ( XY ) =225, then what is…

A: E(X) = 12 E(Y) = 20 E(XY) = 225

Q: 3. If (X(t)} is a WSS process and if 00 Y(t) = | h(u) X(t – u)du, then - 00 (i) Ry (t) = R(T)* h(-t)…

A:

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

A:

Q: af af e. Find g(x,y,z) = af +: az if f = xy²(z³ – 1) | ax ду

A: Given:    f = xy2(z3 - 1)   To find :  g(x, y, z) = ∂f∂x + ∂f∂y + ∂f∂z

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: az Find for z = x²y°e®Y dx

A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: If z =e* + In(xy) Evaluate- ,and ,at the point (1, 2). Hence, calculate the change in z when x…

A:

Q: dz Find if yz – In z = x + y ax

A: To find the partial derivative of z of yz-ln z=x+y with respect x, differentiate yz-ln z=x+y, while…

Q: solve the following P.D.E: azu ди + u at əx² u(0, t) = u(1,t) = 0 (1, 0<x < 1/2 (0,1/2 < x< 1 %3D…

A: In this question, we solve the partial differential equation by the method of separation of variable…

Q: The linear approximation of e is O a. 1.1e O b. 1.1 Oc.e Od.0.1e

A: Linear approximation of e1.1 e1.1=e1+0.1=e1*e0.1=e*e0.1

Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

A:

Q: Which of the following systems is memoryless? O H{x(t)} = exp(x(-t)) O H{x(t)} = cos(t) + x(-t). O…

A:

Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

A:

Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: and further we require that u(r, z) is bounded as z - +oo. Find an expression for the steady state…

A:

Q: Find y' if exy = e 4x -esy-

A: NOTE: Refresh your page if you can't see any equations. .

Q: d If g (x) = ª[e' - In(21 + 1)]dt, find g(x) . dx A e-In(2x+1) 4 (В et + (2x + 1)² 2 (C) (2x + 1)² 4…

A: Topic:- application of integration

Q: For the following PMFS X and Y for k e {0,1,2,3, ..] Px (k) = { %3D otherwise for k e {0,1,2,3, ...}…

A: From the given information, PXk=e-λλkk!, k=0,1,2,3,....PYk=e-λλkk!, k=0,1,2,3,.... If λ=1, a) The…

Q: Find y for the following ey ex-e %3D Select one: 1+y O y= x +y O y = ex-y exy xexy+eY Oy= -yew xexy…

A:

Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: 4 Ruret MC w co , , d, 7 the y a Fid e co f de

A:

Q: then Res(f(z), -1) is ez 1.5 Given f(z) = +1)' А. е, B. C. * _1 D. 0, E. None of the above.

A:

Q: c- Verify Clairaut’s Therom f(s,t) = s²t + In(t²-s)

A: In the question it is asked to verify Clairaut's theorem for the following function given in…

Q: Let w = r. In(xyz), then which of the following is 2 O a. O b.0 O d. O e.

A:

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

A: