Theorem 3-6. If A and B are any two events (subsets of sample space S) and are not disjoint, then P(AU B) = P (A) + P (B) – P(AO R)

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: ST. As in pid. and find the mata'z 3D 3 B such that A- BBT,

A:

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: 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: (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: 1. Write the Null Hypothesis (Ho) or the Alternative Hypothesis (Ha) of the following: 6. Ho: The…

A:

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: 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: are in A.P., b, c, d are in G.P. and at a, c, e are in G.P. -10 - e

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: and xe"y %3D For ay

A: To find out partial derivatives.

Q: Suppose gcd(a, b) = 1. Prove that ab | c if, and only if a|c and b| c.

A:

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.

A:

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

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Q: 1) D Prove that 224 O 210

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: Let A =| 0 -3 0 . Compute A“. 5

A: A=2000-30005 Now,…

Q: If the mean of the following probability distribution is 3.44, what is the variance?

A: Given : Mean = E(X) = 3.44

Q: Obtain the values of In(/3 – i).

A: