Exercise 4.6.9. If a < a', show that D CD7.

Q: 4. Show that for all formulas p, ý, 0 € S(P), (a) (y = ) = ¬(e^ ¬b).

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Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

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Q: Show that E[X]= a +V and o = b 4 4 -

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Q: let f:(a,b)→R be de fined by X€QN(a,b) x€Q' n(a,b) -2 f(x)=' 3

A: This is a problem of Differential Calculus.

Q: art J K

A: j) the mode of the data is 11.5 and it is repeated 15 times in the data

Q: Find the value of c such that enc = 7 c= In

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Q: Let X - N(H, o). Show that the MGF of X is etu+to²

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Q: e Consider the Jollowing fundion. 2= 50x+4, Find the values of d2. az, uwhen oe = 2 and y: 3.

A: Consider the function: z=5x+yx+2y To apply quotient rule of derivatives differentiate the given…

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

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Q: 2. Rv(~C 3. RDL What rule, if any, could you immediately apply to two of the above three lines?

A: Introduction: Some rules of inference: Modus ponens: a⊃ba∴b Modus Tollen: a⊃b~b∴~a Hypothetical…

Q: Show that if E1 and E2 are measurable, then m(E U E2) + m(E1n E2) = m(E1) + m(E2).

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Q: atisfies the given conditions = 30.3°, B = 38.6°

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Q: Show that, for all positive values of x and y, etty > e? ху

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Q: e the coordınates of the Vertlces arter a ection over the 10 6 4 2 10 -8 -4 -2 2 4 8 10 -2 -4 10 6.

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Q: Let c E R and suppose that an → a. Show that can → ca.

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Q: ), then the value of r is

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Q: Suppose T: R + P, has an action on a

A: Given, And

Q: Show that e = o (hª) as h → 0 for all values of q.

A: Like big O notation, there is also a little o notation. There is a difference between big O and…

Q: (b) Use part (a) to show that f (T) is either a transposition disjoint transpositions. or a product…

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Q: In r dr

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Q: 5. If A e U(n) and A e C has length one, show that XA € U(n) .

A: If  A∈∪n and  λ∈ C  has  length one,show that λ A∈∪n.

Q: Differentiate the following with respect to x: b) 3*Inx

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Q: Determine if the following is a fundemental set of solutions to  y'' -6y' + 25 = 0 Given that…

A: If the Wronskian of two solutions is not equal to zero, then the given set of solution is…

Q: (10) If H < Z» × S, with |H| = 12, then H = %3D

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Q: (6) If w = f(u, v), where u = x + y and v = x – y, show that = 2 ди

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Q: (a, o) is not measurable. ylgn ihi

A: Given :-(a, ∞) is not measurable.

Q: Which of these best describes T?

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Q: Under normality, prove the followings (a) B~ N(B,0²(X'X)-)

A: It is known that β^=X'X-1X'Y. Here, Y follows a multivariate normal distribution. The regression…

Q: If S e-t)rLnt dt, Find the valae of (n)

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Q: If z = ax + by and r is the correlation co-efficient between x and y, show that o? = ao? + bo,² +…

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Q: Show that if X gamma(r, A) and Y ~ gamma(s, ) independent, are then X + Y is gamma(r + s, ).

A: X~Gammar,λ fx=λrΓre-λxxr-1,     x&gt;0, r&gt;0, λ&gt;0 Y~Gammas,λ fy=λsΓse-λyys-1,     y&gt;0,…

Q: (c) Deduce that Rn - A < D-a [f(b) – f(a)].

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Q: Please asssit with value for ****,*****, ****** a

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Use the diagram shown. В C 主 G 丰 Which is a needed step to prove that AABF EAEDG

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Q: Let 0 E A C R. Show that if A is both open and closed, then A =R.

A: Given that Let 0∈A⊂R.Show that if A is both open and closed, then A=R. Here we use the principle of…

Q: t, for t > 0, sa X 2 is

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Q: Prove false by creating a counterexample: P(AUB) S 9(A) U 9(B).

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Q: Find the Runet'ion FCA] such that =t+ cost and such that

A: Let y"(t)=d2ydt2=t+cos t and y(0) = 1 and y'(0) = 2 Integrating on both sides, ∫y"(t)dt=∫t+cos t dt…

Q: Given the function z = In (2xy + e3x) - 5y, %3D az a. ax

A: Since, we have to find the partial derivatives ∂z∂x and ∂z∂y of functiongiven by z=ln…

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: et f(x, у, z) %3 ху + z', Р %3D (3, 9, 1

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Q: Given s(t) = t – 6t + 9, evaluate. %3D s(a)

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Q: that H(m m). Show

A: Given function is: Hm=3m-2 We have to find the inverse function H-1m. Let Hm=y Then we get,…

Q: Exercise 9. Use the above formula, together with definition of T, to show that Va(t)||°||a"(t)||² –…

A: Curvature:  If T(t) is the unit tangent vector function to the curve α(t) then the curvature, κ, is…

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: асe of A is

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Q: Consider a S = {x|x"=1} is S, equals to S?

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Q: (b) let ( X, Ź M) be a mea Sure pace for A, BE E Show that MLAUB) = MCA) + M(B) MCANB)

A: since this is a multiple question, as per company policy, we shall only 1 question. If you want any…

Q: Slove the d,e,f part

A: Instruction : Solve the d,e,f part Given Data : d)  Frequency Distribution Table   Class…

Q: Obtain Llerf x; p). Hence deduce the value of Lierf (bx); pl.

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