Let An=[0, (n−1)/n )={x∈R|0≤x< (n−1)/n }, for n=2,3,⋯ Define A = An = A1∪A2∪A3∪... Find A

Q: .If X&Y are independent R.V's,what are the values of Var(X₁+X₂)and Var(X₁-X₂)

A: Solution X1 and X2 are independent random variables then Cov(X1,X2)= Then Var(X1+X2)=Var(X1)+Var(X2)

Q: Show that the set S= {(1, 2, 1), (3, 1, 5), (3, -4,7)} u de nendent where. SCV (B). is linearl

A: We need to find scalars c1, c2, and c3, not all zero, such that   c1(1, 2, 1) + c2(3, 1, 5) + c3(3,…

Q: Evaluate (Vx+ f. d dx. OA. A. Vx2 + 2 + a² - a In + C O B. Vx2 + a² - In |x| C. Vx2 • a? + In- + C…

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Q: Suppose two cellphones are tested at random. We want to find out the number of defective cellphones…

A: Given information: There are 2 cellphones tested at random. D: The defective cellphones. N: The…

Q: A container contains 35 green tokens, 20 blue tokens, and 3 red tokens. Two tokens are randomly…

A: From the given information, there are 35 green tokens, 20 blue tokens and 3 red tokens. Total number…

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: var(û), if û = X1 + a jg X (n-1) + (X2 ++X(n-2) + 3 6X(m-1) + 증 .. 2(n-3) 4. 29n 256(п-3) 29…

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

A: Definition of gcd (a, b) =1 is a and b does not have common prime divisor. Using this we can easily…

Q: Letfandgbetwomultiplicativefunctionsand∈S.Wehavef◦(g◦F)= (fg)◦F.

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Q: Determine whether each is dependent or not, based on the rules for independence. 1.…

A: The data is given as-

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: what is M<E

A: Solution-As the solution is given,

Q: Let 0 &lt; a &lt; b. Use the Mean Value Theorem to show that

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Q: Which of the following sets is uncountable ? Select one: O a. {EN||x − 7| > |x|} O b. R\Z O c. 2Z x…

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Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

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

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Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: let  A= [23−15][23−15]. find||A||1

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Q: Check that P ˅(Q ˅ R) is equal to ┐(R ˄ Q ˄ P) → P

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Q: Prove that |A U B| + |A n B| = |A| + |B|

A: Let A and B are two sets. A = number of elements in the set A. B = number of elements in the set B.…

Q: Let a1, a2, ...,a, be real numbers that are all contained in the interval [-7/2, 7/2]. Use the…

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Q: Find S T(1– a²)+ 5* + 5m(1+ a²)| dæ.

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Q: - (10 points) Show |a – b| < |a| + [b| Va,b eR.

A: We have to show that  a-b≤a+b      ∀a, b∈ℝ

Q: O Is the set S=\[1.2], [-4 2. abaris for R?.

A: We know dimension of ℝ2  is 2  this implies basis of ℝ2 contains two linearly independent vectors.…

Q: (a) If A₁ = {-i, -(i − 1), . . .−3,−2,−1, 0, 1, 2 }, for i = 1, 2, 3,. . . find (i) Un A6 and (ii)…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: X2, ..., Xn, y1, y2, ..., yn, then z is equal to x (A) x + y (B)*+ỹ (C)*+ÿ n (D) x + y 2n

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Q: Let P(C|D) = 0.2, P(D) = 0.3 and P(C|D) = 0.4, then C and D are Select one: a. disjoint b. not…

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Q: Prove that |(a, b)| = |(c, d)| for any numbers a, b, c, d where a < b and c < d. Proof: Prove that |…

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Q: Show that if AB={0}, then P(A)≤P(B).

A: Given that

Q: Let X={x=(x1, x2, X3, X4) : Xi E {1,2,3,4,5,6,7,8,9,10,11,12} for i=1,2,3,4 such that x1 < x2 < X3 <…

A: Given:X={x=x1, x2, x3, x4 : xi∈1,2,3,4,5,6,7,8,9,10,11,12for i=1,2,3,4 such that…

Q: Supppose that X ~ N (2; 3). Find P (1 &lt; X &lt; 4).

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Q: [t was wrong

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Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

A: