Please, I need clear writing if you choose to write by hand for a,b,c, and d.
thanks,
Please, I need clear writing if you choose to write by hand for a,b,c, and d....
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.
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 P(AUB) P(A) P(B) P(AnB). (b) Prove the "union bound," that P(Ai UA2) P(A) +P(A2). Under what conditions does the equality hold?
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.
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2. Let A and B be events. Find an expression for the event "exactly one of the events A and B" occurs; simplify your result as far as you can. Draw a Venn diagram for this event.
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4. Generalize the Bayesian analysis of medical screening given in class. Let a rare disease D occur with probability P(D)-δ, with δ small. The test for this disease is accurate such that the W1 probability of a correct result is 1-e, with ε small. Derive formulas for the probabilities of a true positive P(D +) and a false positive, P(p+). For this screening to be useful...
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2. A device consists of two redundant subunits; only one needs to be working for the device to function. The first subunit has two parts Wi and W2, and the second has two parts W3 and W4. In each subunit, both parts must function for the subunit to work. The four parts are independent identical and equally reliable, with probability p- 0.9 of functioning. (a) What...
After reading the questions carefully, please
prove and compute the questions with clear hand writing.
I need to understand clearly, so when you prove these questions,
please prove it step by step clearly!!!!
3- Let f: [0,1R be defined by f(x) = x2. For each n e N, let P be the partition of [0, 1 into n equal subintervals 3-1) Find formulas for U (f, P,) and L(f, P,). You may use the formula 2 = " n)without proof....
Please I need a very Clean Hand Writing, if you don't
want to write clearly leave it for someone else
Please I need a very Clean Hand Writing, if you don't
want to write clearly leave it for someone else
Please I need a very Clean Hand Writing, if you don't
want to write clearly leave it for someone else
1.18 The graph in Figure 1.6 is the same as Figure 1.4 except that the links have different probabilities of...