For any three events A, B, & D. Such that Pr(D)>0. Prove that Pr(A U B|D) = Pr(A|D) ÷ Pr(B|D) - Pr(A n B|D)

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: Find 3 values of r n =120 o(n) such that

A: Ok

Q: Q.1) Evaluate, (a)/(1+2)*ln (3r) dz

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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: Assume that P(A₁ N A₂ NA3) > 0. Prove that P(A₁ NA₂ NÃ3 Ñ A4) = P(A1)P(A2|A1₁)P(A3|A1 N A₂)P(A4|A₁…

A: We have conditional probabilitiesP() =       (i)P( =                       (ii)P( =…

Q: 5s L |(s – 2)

A:

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: Using the Mean Value Theorem, prove that √1 + x² 0. Make sure to check all the necessary conditions…

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Q: Let X = U(3) find Var(-x) and distribution function.

A: It is given that the random variable X~U(3) Now, in uniform distribution we have two intervals 'a'…

Q: what is the t test for the above

A: A t-test is not appropriate for testing the hypothesis of equal proportions among three independent…

Q: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will throw the same die…

A: Given information: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will…

Q: Let Z∼N(0,1). Find P(-2<Z<1).

A: From the provided information,Z~N (0, 1)The probability P (-2&lt;Z&lt;1) need to be calculated.

Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will throw the same die…

A: Given information: Alan will throw a six-sided fair die repeatedly until he obtains a 2. Bob will…

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

A:

Q: If A = {2,3} and B = {x|x EZ, x<3}, then A x B = Select one: O a. {(1,2), (1, 3), (2, 2), (2,3)} O…

A: If A=2, 3 and B=x x∈Z+, x&lt;3, then to determine A×B.

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

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Q: If E, and E2 are measurable then (E,UE,) is not measurable .

A:

Q: Let n eN 1. Show that o (n²) = ng(n) 2. Show that o (n) +

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Q: A container contains 35 green tokens, 5 blue tokens, and 3 red tokens. Two tokens are randomly…

A: There are total (35+5)=40 non-red tokens and 3 red tokens in the container.  And total (35+5+3)=43…

Q: let  A= [23−15][23−15]. find||A||1

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Q: Calculate P(z<-1.2)

A: The z-score is standard normal variable with mean 0 and standard deviation 1.

Q: P(x) = . Let and let = 10. Find P(9) x!

A: We have to find p(9)

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

A:

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: 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: Drample(2): Determine an even and odd permutations of P- (H W)

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Q: If a z 0, then |a If a < 0, then |a||

A: if a&gt;=0, |a| = ?  if a&lt;0, |a| = ?

Q: A17 Let Xx² (99). What is Var(X)? Answer to A17:

A: X~chi square (99) We have to find var(X)

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

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Q: If m is a positive integer and x > 1, then show that 1-4¹ (-1)" xm+1 m! 2 F₁ m+1 m+2 2 2 dxm

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Q: Let|a| = 32, the number of right cosets of (a²) in is:

A: Given          |a| = 32 Then, &lt;a&gt; = { a , a2 , a3 ,  .  .  .  , a32 = e } ,  where e =…