4. Suppose A, B, C are events such that P(A), P(B), P(C) a. If (A, B,...
(1) Suppose that A and B are events with P[A] = 0.4 and P[B] = 0.7. Show that 0.1 < PAB < 0.4. Justify your answer clearly. P(ANB) - PCA) PCB) = 0.4.0.7 = 0.28 with 0.15 0.28 <0.4 PLA) occuring 04 P(B) occuring 0.7 P of both events occuring at the same time should be = 0.28 which is in Ran 0,4 1028 0.7 2/10
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.
Suppose two events A and B are two independent events with P(A) > P(B) and P(A U B) = 0.626 and PA กั B) 0.144, determine the values of P(A) and P(B).
B] <P[AP[B], and of two events A and B Give an example of two events such that P[ A with P[An B] > P[A]P[B].
3. Suppose that A and B are two events defined over the same sample space, with probabilities P(A) 3/4 and P(B)- 3/8. (a) Show that P(A UB) 2 3/4. (b) Show that 1/8 < P(AB) 3/8 (c) Give inequalities analogous to (a) and (b) for P(A) 2/3 and P(B)1/2.
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.
Problem 7.12. Suppose that f is a bounded function on (a, b) and P is a partition of [a,b]. Show that Lp(f) < Up(f).
Problem 8. Suppose that XGeom(p) and Y ~ Geom(r) are independent. Find the probability P(X <Y).
False Question 3 (1 point) <Venn 5> There are 2 events: A, B with P(A)-0.5, P(B)-0.4, P(AUB)-0.7 Find P(A n B) Question 4 (1 point) Saved <Venn 2 There are 2 events: A, B with P(A)-Q5, P(B)-0.4, PAUB)-0.7
1.14 Consider events ArAg, Avon a sample space Ω. (a) Suppose A, c A-... c AN . Evaluate P(AIA)for i < j and for i > (b) Evaluate the set CAnd D1 A (c) Prove/Disprove: N-1 n AN ) = 1.