Sn =E X;, then the law of large numbers does not hold for the sequence i-1 {S).

Q: Prove kolmogorov's ax

A:

Q: 6. Theorem 131

A: The figure of the circle is given by Theorem : ∠Q = 12mPSR⏜ - mPR⏜ To evaluate : The value of ∠Q

Q: 3- S Srår de

A: Find range of r and theta . Here r varies from 1 to 4 and theta varies from -π/2 to +π/2

Q: Let a = (1,2, 3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) =2(a · b) + (a · c).

A: a=(1,2,3) , b=(1,0,-1) and c=(2,1,3)

Q: . Prove that an→L = Jan] → |L]. (Make cas

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

Q: Prove that: cscz- cot z = 1 2. 2. %3D

A: We need to prove the identity  csc2z-cot2z=1

Q: Prove that {i} = I. ¡El

A:

Q: State the Fermet's Last Theorem. Who was French women mathematican who mede significant 19th century…

A:

Q: 5. Show that () = () +().

A:

Q: Show how James Garfield (1831-1881) proved Pythagorean Theorem

A:

Q: Prove that if gcd (a,b)=1>then gcd (ab,ab)=l

A: I have proved using the fact that gcd can be expressed as integers linear combination q

Q: How many counterexamples are needed to prove that a statement is false?

A: Suppose P(x) be the statement.

Q: State Fermat’s Theorem

A:

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

A:

Q: 8. [ tan’rd.r

A: We have to find the integration of given questions.

Q: Prove that 1lellse TlI

A:

Q: Expend (I+x)

A:

Q: is R* is contractible?

A: This is a problem of Topology.

Q: Show dz 4 In= 는I미페 - for a<0. x <

A:

Q: Given that x, y, and z . Prove that if (x^2)|y and (y^3)|z, then (x^6)|z

A: Solution: The objective is to prove that the given statement

Q: b22 Such that/2/-1E andArg 4.

A: We find complex number

Q: 7. Theorem 94 I (9x-25)

A:

Q: Show that A\ (Bnc) (A\B)U(A\C).

A:

Q: [2 4 21 A = l1 3 1 1 1 B = -2 -1 [2 4 D = 4 C = 1 3 21 -1 %3D 2

A: Given A = 242131B = -1111-2-1C = 242131D = 1-1-1-121 Clearly  C = AD = -B

Q: Find gcd(1000, 34) and lcm(1000, 34) and verify that gcd(1000, 34) · lcm(1000, 34) = 1000 · 34

A: 1000 can be written in the form of prime factors as 1000=2×2×2×5×5×5 34 can be written in the form…

Q: 2017 J Q3 + V5 in the form a+bV5, where a and b are integers. Without using a calculator, express -2…

A:

Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: .Prove that la + b + c| < |a] + |b| + ]c]

A:

Q: Show that (AUB) - (ANB) - CA-B) U (R- A) using laws of Bers.

A: The given question is solved below.

Q: If a =(2,3,-1) ,(1,6,0) ,(2,1,3) prove that Aa^-1 =A^-1A=I Please show all the step

A: Given matrix is, A=23-1160213

Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…

Q: Approximate the value of In (1000!)

A: Given that ln1000!. The objective is to approximate the value. The expansion for…

Q: 1 의( (eat – ebt)} = %3D la-b (s-a)(s-b)

A: Here we have to prove that,  L1a-beat-ebt=1s-as-b

Q: [о, 1] x [1, 2]

A:

Q: Show that Lindeberg's condition follows from Lyapounov's condition.

A: Q