5. In each step, explain clearly what property or axiom you are using (a) Prove "inclusion-exclusion,"...
5. In each step, explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion," that P(AUB) P(A) +P(B)-P(AnB). (b) Prove the "union bound," that P(AiUAz) < P(A) + P(A2). Under what conditions does the equality hold? (c) Prove that, for Ai and A2 disjoint, P(Ai UA2|B) P(AiB)P(A2|B) (d) A and B are independent events with nonzero probability. Prove whether or not A and B are independent.
5. In each step. explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion," that P(AUB) P(A) +P(B)-PAnB). (b) Prove the "uni that P(A UA2) S P(Ai)+ P(A2). Under what conditions does the on bound." equality hold? (c) Prove that, for A1 and A2 disjoint, PAUA2lB)=P(A1B)+P(A21B) (d) A and B are independent events with nonzero probability. Prove whether or not A and B are independent.
5. In each step, explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion,'' that PAU B) = P(A)-P(B)-Pan B). (b) Prove the "union bound" that P(Ai UA2) P(Ai) P(A2). Under what conditions does the equality hold? (c) Prove that, for A1 and A-disjoint, PAUA2B)= PAB)-P(A-B). d) A and B are independent events with nonzero probability. Prove whether or not A and B are independent.
Please, I need clear writing if you choose to write by hand for a,b,c, and d. thanks, 5. In each step, explain clearly what property or axiom you are using. (a) Prove "inclusion-exclusion," that PAU B)-P(A)+P(B)-Pan B) (b) Prove the "union bound" that P(Ai UA2) P(Ai) P(A2). Under what conditions does the equality hold? (c) Prove that, for A and A2 disjoint, P(A UA2 B) P(A B)P(A2 B) (d) A and B are independent events with nonzero probability. Prove whether...
1. Prove“inclusion-exclusion,”thatP(A∪B)=P(A)+P(B)−P(A∩B). 2. Prove the “unionbound, ”thatP(A1∪A2)≤P(A1)+P(A2). Under what conditions does the equality hold? 3. Provethat, for A1 andA2 disjoint, P(A1∪A2|B)=P(A1|B)+P(A2|B). 4. A and B are independent events with nonzero probability. Prove whether or not A and Bc are independent.
2. Prove the three-set version of the inclusion-exclusion principle: using P(AUB)-P(A) + P(B)
I really need someone to solve and explain the last two questions. Thank you! Exercise 1.5. Prove that if A and B are sets satisfying the property that then it must be the case that A - B. Exercise 1.6. Using definition (1.2.5) of the symmetric difference, prove that, for any sets A and B, AAB - (AUB)I(AnB). Exercise 1.7. Verify the second assertion of Theorem 1.3.4, that for any collection of sets {Asher Ai iET iET Exercise 1.8. Prove...
Please explain each step of what you do in detail to solve this problem: 2. (Connected sums) Recall that the connected sum M #M2 of two (path connected) manifolds M and M2 is obtained from the disjoint union of Mi and M2 by removing the interior of a closed n-ball Bi fron Mi (i = 1,2) and gluing together the two boundary (n 1)-spheres by a homeomorphism π1(M,,p) *n(My, P2), Prove for appropriate base point p provided n 2 3....
Please solve it step by step and clearly. Thank you. 5) Where do Americans tend to fall on the conservative-liberal political spectrum? The General Social Survey asks, “I'm going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal, point 1, to extremely conservative, point 7. Where would you place yourself on this scale?”. The table shows the seven-point scale and the distribution of 1933 responses for a survey conducted...
Please explain clearly and show each step for how to do this problem please!! Thank you so much ! Tiger Company sold 1,000,000 boxes of cereal under a new sales promotional program in 2019. Each box contains one coupon, which submitted with $2.00, entitles the customer to a stuffed animal. Tiger pays $4.00 per stuffed animal and $1.20 for handling and shipping. Tiger estimates that 40% of the coupons will be redeemed, even though only 100,000 coupons had been processed...