17. Given: FG || KL, FG = KL Prove: AFGK = AKLF

Q: let x~ exp0), find B.C.R to test Ho: O3 against H,: 0 2,if4, ds o.05,

A: Exponential distribution: Here, X1, X2,,…, Xn, are iid (independent and identically distributed)…

Q: If A₁, A, E and P(A) = P₁, P(A)= P₂, show that P(A₁4₂)≥ 1- P₁ - P₂. (Hint: Use DeMorgan's Law (44₂)…

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Q: Using Boole's Rule, Evaluate (x² + 3y²)dxdy

A: Given:                ∫02∫0yx2+3y2dxdy To do: Evaluate the integral using Boole's rule.

Q: Suppose n E N and u, v € V₁ such that |u| = 5, |v|= 4 and u⚫v=-7 Find |3u + v. Find t R such that u…

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Q: Let a,b,c eZ. If a|b and a |c then a' |(b² =c² ). nsi2

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Q: 4 1 0 Let X be N , ( μ. Σ ) with 1 30 0 0 2 Examine the independence of the following : (i) X, and…

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Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: Ź uk=2='In, find u00 u 100 Suppese that

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Q: Given that w = f (u, v) And u = xz. , V = dw = X az aw aw Prove that Z - ду

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Q: Evaluate $ c TZ e cusz -dz DCi |Z=1|=1 ✓ C₁ | 2+1 | = |

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Q: Show that for all v in Rn, II v II s <= II vII m·

A: vs represents the "sum norm" or "L1-norm" and vm represents the "max norm" or "L infinity-norm".To…

Q: is equal to where A = = and where B= In(r7s²r683) Alnr + Bln s

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Q: S 289 xe

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Q: Let Z - N(0, 1). Find P(Z < 2). Question Help: D Post to forum

A: Given that, Z~N(0,1)

Q: When the null hypothesis is rejected, then:    A. F>F(α,n-k,k-1)  B. F>F(α,k-1,n-k)  C. F = 0  D.…

A: We will find the rejection region in ANOVA table.

Q: Show that for all v in Rn, llvllE&lt;= √nllvll m·

A: we have to prove the inequality: we know that, We start with the definition of the Euclidean norm of…

Q: 2 and y = If x:y:z 4:6:9 and z = 45, then x =

A: Given:          x:y:z=4:6:9     and   z=45To…

Q: sst. Let f(x, y, z) = x³ yª + zª and x = s5, y = st³, and z = s

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Q: FOo=X-1 de fined 2n E- lro] show that Fis Riemenn integruhk

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Q: 6. Given: AUVW = AXYZ Prove: UV || XY .Y W

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Q: 1. Let A=(a)xn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. |a|< (aa)², i,…

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Q: M [e-ax; p] = Гр) Re (p) > 0

A: It is a simple, formula based proof by using laplace. Mf(x); s= ∫0∞xs-1f(x) dxM[e-x; p] =…

Q: 43 If uzzt+y+z , u?v =y+z,u³w=z, Show that a (x,4,z)

A: Q3. Here, u=x+y+zand,u2v=y+z⇒v=y+zu2=y+z(x+y+z)2and,u3w=z⇒w=zu3=z(x+y+z)3

Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: What are the consequences of the violation of the OLS assumption cov(x;, e;) = 0?

A: A linear Regression  model consist of one dependent and one independent  variable.

Q: Let f(x) = VT, 9(x) = ,. , andh(x) = x². (h o ((h o go f) – f)) (4) = %3D 5-x Select one: a. 4. 81…

A: let f(x) = x , g (x) = 45-x and h (x) = x2f (4) = 4= 2g (f(4) = g2= 45-2= 43h (g(f(4)) = h 43=…

Q: Let f(x) ={ 2+ Vex-x , for os x 2 } 2 4 evaluate fCx) dx and I f6) dx

A: Given piece wise function as, f(x) = 2+2x-x2    for  0≤x≤24-x                  for  x &gt;2we need…

Q: Ex let x be with pmf 1=,2,3, 16 O find c P(X)2)

A: We want to find the value of c and P(X≥2) and P(X2=9)= ?

Q: 13. Prove or disprove: Q/ZQ.

A: (.) We have to prove or disprove .

Q: u = 3, o2 = 9, P(-6 < X<12) a. Determine P(u – ko < X<u+ ko) 1 - 1/k?

A: According to the Chebyshev's theorem, 1-(1/k²) of the observation fall within k standard deviation…

Q: s) Let ICS(P), 4,0, € S(P), and let I (p = 0). (a) Show that then riff I and (b) r, iff r, 0.

A: As per the question, we have to prove two statements related to the consistency of deductive…

Q: Let A = {m CZ/m = 4k+8} where k CZ, and let B = {n CZ/n=2r + 2} where r CZ. Show |A| = |B

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Q: 2 1] Assume A = 1 3 4. [2 2 4 and B = show that (AB)' = B' A' [3 6 4]

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Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Let f(x, y) = x for y=0 and 0 for y+0. Evaluate each of the following or if they do not exist, state…

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Q: If S:= {1/n - 1/m²n,mEN }, find inf Sand sup S.

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Q: Prove the given statement by the indicated method. (1). By Direct Proof: "Vm,n € Z*,+> 2."

A: ∀m, n∈ℤ+,We know square of an integer is always non-negative Hence (m-n)2≥0…

Q: Let A and u be positive real numbers. Then Jp(Ax) and Jp(ux) satisfy d d + dx dx (11.6.37) d ( d p²…

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Q: let 19, b) = 1, them prove that there exists x20 Such that ijzo ax_by = 1

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Q: -3 < x To nenen Is fox is odd ? even or

A: Use definition of odd and even .

Q: Consider the following statements: P:x is odd, Q: x is positive, R: -4 <x < 3, S: æ| < 2. Find all…

A: The given statement is a logical if-then statement. So this statement becomes false only when S is…