Example 3: If x1, X2 , ... , Xn is a random sample from a normal population .2 N(µ,1), show that t=- E x is an unbiased estimator of u +1.

Q: What are the right three digits of 3402? Hint. Use Euler's theorem. What is o(1000)?

A:

Q: Compute the following. 4! 6! ]*

A: Answer - First we need to understand what is factorial before solving this question  n!…

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: Let A = [0, 1] – Q. Determine if A is countable or uncountable. Prove your claim.

A: Let

Q: 1. Prove that the followingn is a theorem in SD. Av - A

A: Theorem :-

Q: If continuous or f differentiable is [ Select] on [a , b] then the [Select ] integral of definite or…

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Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

A:

Q: Is Statement (1) below True or False and WHY? TEA=B is equivalent to "TEA IFF TE B"

A: Let us provide justification and check whether both equations are equivalent or not

Q: Let a e Z. Prove that if 6 | a and 10 | a, then 15 | a.

A:

Q: (b) Let a.. and m be positive integers. Prove that if (a,m) = (b, m) = 1, then (ab, m) = 1.

A: Given  a, b and m are positive integers.  (a, m) = (b, m) = 1.We have to prove that (ab, m) = 1.

Q: Consider the following. Find Av. Av= 7 1 10 -1 -HD] 1 1 1 - [3 A = Complete the following statement.…

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Q: If P(A) = P(B) = P(AB), show that P(AB + AB) = 0 [AB = An B]. %3D

A:

Q: Let x € Z. Prove that if 3x + 7 is even then x is odd.

A: , then we have to show  is even then  is odd

Q: Prove that if A and B En and Ac B, then

A:

Q: Prove ImA = A = Aln if A is m X n

A: Given: A be m*n matrix

Q: Prove the following: P(n,r)=P(n-1,r)+r.,P(n-1,r-1)

A: Recall: P(n,r ) = Prn=n!(n-r)! n! = n(n-1)!

Q: If z1:2., are complex numbers such that =|= =. = |=,| =1, Prove that

A: To prove: z1+z2+…+zn=1z1+1z2+…+1zn Given: z1=z2=…=zn=1 Since, (1) zz¯=|z|2 (2) z=z¯

Q: Let ā= . Find |āà.

A: Here we will find the magnitude of vector a,

Q: Compute the following. 8 (²) 5

A:

Q: Prove the following claim: At least two powers of 3 have exactly 100 digits

A: The number of digits in an number x is log10x+1, where · is the greatest integer function. The Claim…

Q: Given A = 03-2 00 1 compute et.

A:

Q: Suppose that P(A;) = 1 for all i = 1, 2, .... Show that P(N A;) = 1.

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Q: Let a e Z. Prove that if 7 | 2a, then 7 | a.

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Q: Evaluate the following E jOO) i() ())]

A:

Q: 3. Prove: P[N=1 Ak] >1- £P[A]

A: Boole's inequality(or the union bound) states that for any at most countable collection of events,…

Q: .

A: Given, The matrix,

Q: Obtain the values of In(/3 – i).

A: