If X₁ and X₂ are independent rv's then Px₁+x₂ (t) = x₁(t)¶x₂(t) More, generally for independent rv's X₁; i=1,2,…,n, we have Px₁+x₂+...+X₂ (t) = x₁(t)¶x₂(t)….. Oxn(t)

Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: If (x, y)= x²y+e* , find; d. y е. b. $, с. Ф Q.4 (1)

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Q: If X = x „then W(x1(t), x,(t)) = 10 Select one: O a. ce- а. O b. ct C. c t? d. ce'

A: We will use basic knowledge of Wronskian for a II order linear homogeneous ODE. WE convert the above…

Q: help please answer in text form with proper workings and explanation for each and every part and…

A: The given heights are: 80, 71, 68 80, 71, 67 78, 71, 67 76, 71, 67 75, 70, 67 75, 70, 66 75, 70, 66…

Q: Prove that (C, +) ≈ (R × R, +).

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Q: • Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

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Q: If f-(a, b) = 0 and fy(a, b) = 0, then Vf(a, b) = 0.

A: Given,           fxa,b=0   and   fya,b=0

Q: 4. (a) Prove, without recourse to geometry, that u • (v × w) = v • (w × u) = w • (u × v) = −u • (w ×…

A: Solution: To  solve  the  above  problem,  we  need  a  basic  result .Let  us  recall  that  first…

Q: If f(r, v)= +y-2y, find fa (2, 1), f (2, 1), fay(2, 1) and fy(2, 1).

A: Given a function f(x,y)= x3+x2y3-2y2 Now, fxx= ∂2f∂x2=∂∂x∂f∂x fyy= ∂2f∂y2=∂∂y∂f∂y…

Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: (3) Let X n(µ,4) and Var(2x)= E(5-8x) find u.

A: Given that X follows normal distribution with mean mu and Variance 4 E(X)= mu Var(X)= 4 Given that,…

Q: If r(t) = (1,r ,t), then r'(t) equals (a) (1,21,-2r"). (b) (0,21,–21 ") . (e) (0,21,-21 *).

A: Given that: r(t)=1,t2,t-2Differentiate both sides with respect to…

Q: 4. Let S and T be stopping times for a filtration (Fn). Let M N = max(S, T). (a) Show that M and N…

A: Since I have solved similar ones,let us solve the problem step by step by proving m and n are both…

Q: What are the coordinates of C' after its preimage, C(5,-3), is reflected over the x-axis? O (5,3) O…

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Q: What are the assumptions needed for testing two population means from independent samples?

A: Statistical hypothesis testing is an important method in inferential statistics. It is used to test…

Q: Given a p.m.f. f(x) of a d.r.v. x as follow: x = 1,4 f(x)=5 0 O. W

A: Moment Generating Function (MGF) The moment generating function (MGF) of a random variable X is a…

Q: S(x,y,z)= hn xyz +e (30) find f,, and f. 4

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Q: Find (r.)ifr=√.e and r₁=(. In (21)) r, dt

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Q: If f(x,y,z) = e* and g(x,y,z) = y – z Then, V (fg) will be;

A: Given fx,y,z=ex, gx,y,z=y-z

Q: S f(t) dx = 0. 1.

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) =i - 3tj + K 2 (a) r'(t) (b) r"(t) (c)…

A: Given that, r(t) = (3t2/2)i - 3tj + (t3/2)k   Ans (a). first derivative of the function, r'(t) = 3ti…

Q: If the Equation Hx = c is inconsistent for some c in Rn, what can you say about the equation Hx = 0?…

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Q: af (8,9). Let f(x,y)=x?y*. Find ду

A: We are given: f(x,y)=x2y4 ⇒∂f∂y=x24y3=4x2y3

Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: Let r(t) = Find i'(t) F'(t) = < V

A: Consider r→(t)=4t4-2,3e-2t,-4 sin (5t) we have to find r→'t

Q: If r(t) 0, show that r(t) = r(t) · r'(t). ‡

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Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: The covariance of X1 and Xzis defined by cov(X, X,) .A .B E[(x, -x,)=] .C E[(x, - x,)] .D

A: Option D is correct.

Q: Let f(x, y) = x² e". What is fx(3,0)? Select one: O a. 0 O b. 6 O c. 9 O d. Not defined O e. None of…

A: We have to find the value

Q: Let f(x, y, z)= and c(t) = (t, 13/2, t). Compute ff ds y+z

A: The given function is fx,y,z=x+yy+z, and the curve is given by c(t)=t,23t3/2,t. To Evaluate:…

Q: If P(A')= 0.4 and P( A and B)= 0.30, then find P(B|A)?

A: Answer: From the given data, P(A') = 0.4 Since, P(A) + P(A') = 1 P(A) = 1 - P(A') = 1 - 0.4 = 0.6…

Q: If f(u, v) = 3uv³, find the following. i f(3, 1) = i fu(3, 1) = i f,(3, 1) =

A: We have to solve