4. (a) Show that (b) Two events A and B are said to be conditionally independent...
Recall that two events A and B are conditionally independent given an event C if P(A∩B|C)=P(A|C)P(B|C). Prove that P(A∩B|C)=P(A|C)P(B|C) if and only if P(A|B∩C)=P(A|C).
Prove that (for two events A and B) if A and Bc are independent, then A and B are independent
6. Suppose events A and B are conditionally independent given C, which is written ALBIC (a) Show that this implies that ALBIC and ALBIC and ALB-|C, where A means "not A." b) Find an example where ALBIC holds but ALBCE does not hold
Prove that if A and B are independent events, then (a) A and B are independent. (b) A and Bc are independent.
2. Suppose A, B, and C are events of strictly positive probability in some probability space. If PAC) 〉 P(BC) and P(A|Cc) 〉 P(BİC"), is it true that P(A) 〉 P(B)? If P(AC) > PlAIC") and P(BIC) > P(BIC"), is it true that P(An BC) > P(An BIC)? 2. Suppose A, B, and C are events of strictly positive probability in some probability space. If PAC) 〉 P(BC) and P(A|Cc) 〉 P(BİC"), is it true that P(A) 〉 P(B)? If...
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)
How can I prove this? 2. (one point) Show that for any three events A, B, and C with P(C) >0, P(A U B|C) = P(A|C) + P(BIC) – P(AN B|C)
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.
3. Given that A and B are independent events, show that: a) A and B' are independent b) A' and B are independent c) A' and B' are independent
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)