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 ÑA₂ Ñ A3)

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: Suppose P(A) = 0.24 and P(B’ ) = 0.48   (a) Find P(A ∪ B) if A and B are independent. (b) Find…

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Q: HW 2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 <Z< 2) c) p(-2 <Z < 1)

A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

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: HW_2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 < Z < 2) c) p(-2 < Z < 1)

A: Solution

Q: Which of the following is not equal to P(100, 2)? 2P100 100! 98! 9900 100P2

A: We have given, P(100,2) The number of permutations of n things taken r at a time is defined as,…

Q: answer

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Q: (6 y x - 2 y)d A R=[1, 4]×[0,3] 9 .A O 9 2 .B O 2 9.

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Q: from x = 2 to x = 10 and x; is any value of x in Ex¡. Express lim s as a definite integral. n-x n D…

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Q: 7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . • (a) Find P(A¹) . . (b) Find P(A and B) (c)…

A: Given data, p(A) =13p(B)=12p(A∪B)= 23we have to find out the given probabilities.

Q: Suppose that 7 '(t) = and 7 (0) = . Find 7(t) 7(t) = <

A: Suppose that r→'t=12t,e0.2t,t and r→0=1,-1,4. Then we have to find r→t=?

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: Find the L(e2" (1+ t)²). ,2t a) + (s-2)* 1 b) + (s-2)2 2 (s-2)3 (s-2)2 c)+2 (s+2)³ (s-2)? d) +…

A: The following formulas can be used to obtain the Laplace transform.…

Q: Q3: If P(X= x) = a 8(x) + b 8(x + 1); then a + b = A) 0.5 B) 0.3 C) 0.4 D) 1 E) None

A: Given: P(X=x)=aδ(x)+bδ(x+1)

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: (c) Check whether or not: Q (2¹/³) = Q(4¹/3) Also obtain (Q (2¹/³): Q].

A: We first find [Q(2^(1/3)):Q]  Then using this prove that Q(2^(1/3))=Q(4^(1/3))

Q: Let B = {1-3t +t² , 2 - 5t + 3t2, 1 + 5t2} and p (t) = 2 – 5t + 4t. Find x [p]g. %3D X1 = X2 = X3 =…

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Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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

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Q: Let a ER and set fa: R→R: xx+1|-2|2x|+ a. S(a)= {r ER: fa(x)=0}. (So, S(a) is a set). P= {a € R:…

A: Given information fa : ℝ→ℝ  : x→x+1 -22-x +a Sa =  x∈ℝ : fax =0  P =  a∈R : Sa = ϕ Qa =  x∈ℝ : fax…

Q: T 8-1 H = 2 1 & T = 6 5 Find T TB] (NO guess and check on linear combinations!)

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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: Q2 (Bayes' Theorem) It is given that P(B|A) – 0,15. P (B|A) = 0.03 and P (A) = 06. Compute P(A|B).…

A: Ac=A bar  P(B/A)=0.15, P(B/Ac)=0.03, P(A)=0.60, P(A/B)=?

Q: X1 Xi + 2x3 , X1, X2, x3 ER – 4.x2 T: R³ → R², T x2 X3 - x3 ||

A: So first we prove that the given transformation is linear

Q: Let X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently. 1.…

A: X1 ∼ N(0.7,1.4), X2 ∼ N(−0.5,1.2), X3 ∼ N(0.9,1.7), and X4 ∼ N(−0.2,2.1), independently.

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

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Q: Show that |Z × Z|=|N|

A: ℤ represents set of integers ℕ represents set of natural numbers  To show ℤ×ℤ=ℕ We know that|ℕ|=α0…

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

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Q: (5) {1,2} C P({1, 2}).

A: Given  set is {1,2},  we knew that power set of a given set is set of all subsets of the given set.…

Q: let x be have P.dif 0 < x <3 f(x)= ={th find The U.b. of P(IX-M73) and find The L. b.

A: Please see below

Q: Find P(C/A) and P(C) if p(A1) = 0.6 B1 0.8 0.7 C1 A1 C2 A2 0.7 B2 0.8 %3D [Hint: P(C/A) =…

A: Probability mass function P(X=xi) Simple facts about pmf  ∑(X=xi) =1iP(X=xi ∩ X=xj)=0 if i≠jP(X=xi ∪…

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

A: Given that

Q: Let A = {a, b}, B = {x, y}, C = {x, z}. а) (6.1 #32b) Find P(A x B). a

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Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus