11 If P(A) = , P(B) 3 and P(A U B) = 4 find (i) P(A/B), (ii) P(exactly one of A and B occurs). 12 (iii) whether B is independent of A.

Q: 10. x(x² + y²)²Cydx – xdy) + yºdy = 0.

A:

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

Q: the second

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Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

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Q: 2: Find: L-¹ [- S3 1

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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: [2 3 2. Given A = 30 2 B = C= -2]. Verify that (AB)C = A(BC) %3D

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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: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

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: 1. Flip three coins and let Y be the number of heads that appears. Then flip Y coins and let X be…

A: Given Information: Three coins are tossed and Y is the number of heads that appear from this trial.…

Q: Suppose P(X) = 0.35 and P(Y) = 0.40. If P(X|Y) = 0.28, what is P(Y|X)? O (0.28)(0.40) 0.35 0.28 0.35…

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Q: 2: Find: 1 [53 - 3] L-1[:

A: We are required to find the inverse Laplace transformation of the function 1s3-a3 i.e. ℒ-11s3-a3 .…

Q: 14. Given P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?

A: Given that: P(A) 0.25 P(B)=0.28 P(B|A) =0.28

Q: (5) If X is the number of heads obtained in four tosses of a coin, the mode of Y = is: 1+X

A: X is the number of heads obtained in 4 tosses of a coin. Here the total number of trials is n=4. We…

Q: 10 2. F (s) s2 +4s+4

A:

Q: Given a p.m.f. f(x) of a d.r.v. x as follow: x = 1,4 f(x)=5 0 O. W

A: Moment Generating Function (MGF) The moment generating function (MGF) of a random variable X is a…

Q: ) plt)=4-5; Find p(i – 2)

A:

Q: If w(f.9) = , then w(s.S+9) = (A) (B) - (C) 22 (D) -22 (E) None

A: Ans:- If w(f,g)=x2, then we have to find the value of w(f,f+g).

Q: (8) IF: A=i+j+ k, B = i +2j - 3k Find A-B, A.B, 2A.3B, A.B, (A+B). (A-B)

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Q: Suppose P(A)= 4, P(B)= .5, following: Find the P(ANB) a. b. P(A'nB) с. d. P(A'UB') P(BA)

A: Comments: As per our guidelines we are supposed to answer only first three subparts. Kindly repost…

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: In the morning section of a calculus course, 2 of the 9 women and 2 of the 10 men receive the grade…

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

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Q: L-1 if (24/ ((5-7)²-9) 1 ;)} What's the value of a*c? = atbect senh(3t). =

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Q: If C(12,4)+C(12,5) = C(n, 5), then n is equal to

A:

Q: Suppose A and B are independent and mutually exclusive. P(A) = 3/10. Can you determine P(B)?

A: GivenA and B are independent and mutually exclusive eventsP(A)=310

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

A:

Q: [1 3 0] If A = 1 2 1, then the Accompanying worker for Lo 1 4] 1. (a2,) | A. -4 В. -12 2. (a32) 3.…

A:

Q: 8Given that p(A | B)=0, and p(A)=.15, (a) independent? (b) exclusive? are A and B

A: we know that if two events A and B are independent thanP(A|B)=P(A)and P(B|A)=P(B)  If two events A…

Q: (7) Let X = P(2) and E-x)= E(5– 5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of…

A: Given X~Pλ and E15x=E5-5x

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: 7. Show that (a). (Z, +) # (Q, +). (b). (Q,+)# (Q\{0},.). (c). (R\{0},-) # (Q\{0},.). (d). (R\{0},-)…

A:

Q: 5. Given that C and D are independent and P(C | D) = 2/3        P(C ∩ D) = 1/3 find (a) P(C) (b)…

A: Given that, P(C|D) = 23 P(C∩D)=13