If P(E)9 and P(F)-.8, show that P(EnF)2.7. I inequality, namely, n general, prove Bonferroni s Use induction to generalized Bonferroni's inequality to n events and show the result.
[15] 4. Let E and F be events of sample space S. Let P(E) = 0.3, P(F) = 0.6 and the P(EUF) = 0.7. a) Fill in all probabilities in the Venn diagram shown. S b) Find P(EnF). c) Find P(ENF). d) Find the P(E|F). e) Are E and F independent events? Justify your answer.
10. Prove that P(E UFUG)P(E) P(F) + 2P(EFG). 11. If P(E)9 and P(F).8, show that P(EF .7 In general, prove Bonferroni's inequality, namely, P(EF) 2 P(E) + P(F)-1 13. Prove that P(EF*)= P(E)-P(EF).
e and E and P events associated with S. Suppose that Pr(E)-0.5, Pr(F) -0.4 (a) If E and F are independent, calculate: i. Pr(EnF) ii. Pr(EUF) iii. Pr(El) iv. Pr(FIE) (b) If E and F are mutually exclusive, calculate: i. Pr(ENF) ii. Pr(EUF) iii. Pr(E|F) iv. Pr(FIE)
3) Prove the expression (p – 1)(p − 2)(p – 3) ... (p – k). -; where k sp - 2, k a whole number. (k + 1)! is an integer whenever p is prime greater than 2.
Please prove problem 151: parts a, b and c. If its not too much trouble, please prove the contrapositive of the statement proved in 151. 151. In this problem we will prove the following statement: Let E CR be nonempty and let f : E -> R be a continuous function. Then if f(E) is not a connected set, E is not a connected set as well (a) Suppose that f(B) = AUB where A and B are nonempty sepa-...
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(3) Suppose that f E C'((0, 1]). Given e > 0, prove that there exists a polynomial p such that lf-plloo -p'| <E (3) Suppose that f E C'((0, 1]). Given e > 0, prove that there exists a polynomial p such that lf-plloo -p'|
Prove or Disprove: Let p E P(F) and suppose that deg p > 1 and p is irreducible. Then p(a)メ0 for all a E F.
answer all 34. What is the hybridization of the phosphorus atom in PC13? a. sp b. sp c. sp d. sp'd e sp'd c. 35. What hybridization change does the carbon atom undergo in the combustion of methane? CHa() +202g) CO(g)+2H20() Copyright Cengage Leaming. Powered by Cognero. Page 7 Name: Class Date d sp sp bspp C. sp + sp d. sp +sp e. none 36. How many sigma and pi bonds are present in H2CO? a. 1 sigma bond...