6. Suppose events A and B are conditionally independent given C, which is written ALBIC (a)...
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
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).
4. Consider events A and B. Let C be the event that where either A occurs or B occurs, but not both. Show P(C)- P(A) P(B) - 2P(An B). Compute P(An B) and P(AlB) chance of being male. Let A the event that there is at most one female. Let B be 5. Consider events A and B. Suppose P(A)0.2, P(B)0.3 and P(AU B)-0.4. 6, A cat has a litter of kittens. Each kitten has a 50% chance of being...
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
In a sample space, events A and B are independent, events B and C are mutually exclusive, and A and C are independent. a) Show that P(AUB) = P(B) + P(A)P(B') = P(A) + P(A')P(B) b) If P(AUBUC) = 0.9, P(B) = 0.5 and P(C) = 0.3 find P(A).
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)
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
4. Suppose A, B, C are events such that P(A), P(B), P(C) a. If (A, B, C) are independent, show that P(AU BUC)- b. If A, B, C are only pairwise independent, show that 17 24 SHA UBUC)<19 24
Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs and mutually exclusive. P(A)=0.78 P(B)=0.34 PC) -0.21 P(BA) =0.78 P(CB) =0.21 PAC) =0.21 Elect all that apply: O A and C are independent O A and B are independent O A and B are mutually exclusive OB and C are independent
Classify the events as dependent or independent: Events A and B where P(A) = 0.5, P(B) = 0.2, and P(A and B) = 0.09 Independent or Dependent? 0.5 x 0.2=0.10 which does not equal 0.09, does this mean that the correct answer is dependent?