(1). If we toss a fair coin 3 times, let X and Y be the number of heads and the number of tails respectively. Compute E[XY].

Q: Q7 Assuming y = f(x), compute [3xy²] dx

A: The function is y=3xy2.To find : Compute ddx3xy2

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: 2. Determine the power set p(A) = {{a, b}, {c}, {d, e, f}} 3. Suppose A = [7, e,0} and B = (0,1}.…

A:

Q: Give four different ways to determine when A = M₁ (F) is singular.

A: To determine the different ways when A∈Mn(F) is singular .

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

A:

Q: Prove that CL dx = ln lx1+C. Chint): set x

A: Please refer to the image below.

Q: 1. a) Find the mean value u of the function f (x) = |3x| +3 on the interval [-2, 1] . %3!

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Q: For the function f(x.y) = e 4xy, find f, and f,. f, =

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Q: 7. Find Lt V1+P

A: Introduction :

Q: Calculate , if xyz Ax, y,2) = x² – x²y³ -2 3 = x -x y -Z A.5 1 C. No one correct. В. D. E. 7 Е.

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Q: TOPIC: SETS 1. List the elements in the set. (x x < 3and xe Z) 2. List the elements in the set. (x 2…

A: To list the elements in the given set (1) x;x&lt;3 and x∈z

Q: 1. Evaluate: e 3z I = dz (e² + e5z)2

A: given integral I=∫0∞e3zez+e5z2dz claim- evaluate the integral

Q: Vz²+1 ev° dy In a

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Q: The joint density function of continuous random variables X and Y is given by: cxy, 0 1).

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Q: Find y" if y = (1+1)²+√√t when t = 1. a. 3.5 O b.2.25 O c. 2.25 O d. 1.75

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Q: a) Ignore the birth weight (x). If the length of gestation are independently and identically…

A: Reviewing information, x={60,110,44,900,107} y={122,241,61,365,617} n=5 The fitted model…

Q: 41. Find a formula for the function S(x, y, z) of three variables that gives the average of three…

A: We have to find the formula for function S(x, y, z).

Q: II. Evaluate the following. 1. z = ji

A: Given: z=jj

Q: determine f ∗g. Q. f(t)=t, g(t)=1.

A:

Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

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Q: -dz < 2re?. z + 1 Jェ-1|=1

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Q: Differentiate g(t) = -8/t .

A: Known fact: ddxx=12xddxkfx=kddxfx

Q: Liouville function X(n) is given by formula

A:

Q: C) Find S x²e¬x dx

A: Integration by parts formula:

Q: Compute e-1/z ₁-3+1° -dz, and $ e¹/2² |z-i|=3/2 2² +1 dz.

A: Concept Used If a complex function f(z) is analytic within and on a closed contour c inside a…

Q: =gers and

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Q: a) Find the values of A and B if - {(x² + Ax + B)e*} = x²e* dx Hence, evaluate S, x²e*dx

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Q: If z is implicitly defined as a function of x and y via the equation e² = xyz, compute 33 and 3.

A: The given equation is, ez=xyz. To find: ∂z∂x,∂z∂y. To compute ∂z∂x,∂z∂y : Partially differentiate…

Q: Q: Examine y (o.4), Using Runge - Kutta Order 4 method if X = 4n + 2

A: Given y′=4x2+2y,      y(0)=1,   h=0.1,   we have to find y(0.4).Forth order R-K…

Q: Find the pro ection of v on the line with equation

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Q: If f(x, y) = x²ye*xy, find fx and fyx.

A: Given function is