Prove that (for two events A and B)
if A and Bc are independent, then A and B are independent
Prove that (for two events A and B) if A and Bc are independent, then A...
Prove that if A and B are independent events, then (a) A and B are independent. (b) A and Bc are independent.
4. (a) Show that (b) Two events A and B are said to be conditionally independent given C if P(An BIC)P(A|C)P(BC). Prove that if A and B are conditionally independent given C, then
Prove or disprove: Two events A and B are independent if and only if they are disjoint.
1. Consider two independent events, A and B, where 0< P(A) <1,0< P(B)< 1. Prove that A and B' are independent as well.
Consider two independent events, A and B, where 0くP(A) < 1,0くP(8)く1. Prove that A' and B' are independent as well.
Suppose A and B are independent events. In expression (1.4.6) we showed that Ac and B are independent events. Show similarly that the following pairs of events are also independent: (a) A and Bc and (b) Ac and Bc
Consider two events A and B whose probabilities are known. It is known that the two events are not mutually exclusive and not independent. Which of the following calculations could be used to compute P(A ∩ Bc)? P(A ∩ Bc) = P(A) + P(Bc) P(A ∩ Bc) = P(A) • P(Bc) P(A ∩ Bc) = 1- P(A ∩ B) P(A ∩ Bc) = P(A) - P(A ∩ B)
If A and B are two independent events together with ?(? ??? ?) = 0.6 and ?(?) = 0.7, calculate ?(?). If A and B are two independent events and ?(?) = 1 2 and ?(?) = 1 5 , find ?(? ??? ?). Given that ?(? ?? ?) = 0.86, ?(?) = 0.79, and ?(? ??? ?) = 0.41, find ?(?).
a. Prove: If A and B are independent, then so are A and B. b. Prove: If A and B are independent, then so are and . c. Give an example of events A, B, and C such that but We were unable to transcribe this imageWe were unable to transcribe this imageP(An Bn C) = P(A)P(B)P(C), P(AnBn C) P(A)P(B)P(C) P(An Bn C) = P(A)P(B)P(C), P(AnBn C) P(A)P(B)P(C)
2.30 Probability of independent events. Given two independent events A and B with PIA 0.3, PB 0.4, find (a) P[AU B; (b) P[AB); (c) P[BIA); (d) P BA)