Let A {p, q, {p}, {g}, {p, q}} (a) Is {p}C P(A)? (c) Is {{p}}€ P(A)? (d) Find all the three element sets in P(A) (b) Is {p} € P(A)? (e) Find all sets B such that B C A and {p, {p}}C B.
Evaluate p(P), p(QU), p(PQ,U) with the following figure: p) 0.0S p(R) 0.01 R P(PiR,) 0.95 P(PIR,) 0.90 P(PI-R,0.01 P(UIP)0.7 P(Ul-P)-0.2 u p(VIS) 0.99 v^ P Evaluate p(P), p(QU), p(PQ,U) with the following figure: p) 0.0S p(R) 0.01 R P(PiR,) 0.95 P(PIR,) 0.90 P(PI-R,0.01 P(UIP)0.7 P(Ul-P)-0.2 u p(VIS) 0.99 v^ P
Prove that 1-[p(1-p)^0+p(1-p)^1+p(1-p)^2+p(1-p)^3...+p(1-p)^n]=(1-p)^n using geometric series equation.
Suppose A,B, and C are events such that: P(A)=P(B)=P(C)=0.3, P ( A ) = P ( B ) = P ( C ) = 0.3 , P(AB)=3P(ABC), P ( A & B ) = 3 P ( A & B & C ) , P(A∪C)=P(B∪C)=0.5, P ( A ∪ C ) = P ( B ∪ C ) = 0.5 , and P(AcBcCc)=0.48. P ( A c & B...
3.9. Given P(A 0.4, P(B) 0.5, and P(An B)-0.2 verify that a) P(A B)-P(A) b) P (A |B)-P(A) c) P(BlA) P(B) d) P(BIA) P(B) 3.10. If the events A and B are independent and P(A) 0.25 and P(B)- 0.40, find a) P(An B) b) P(AB) c) P(AUB) d) P(A nB)
2 P(A) = = ,P(B) = 1,P(A1B) ,P(AB) + P(BA) Find P( AUB 3
Show that P(A∪B) = P(A) + P(B)−P(A∩B)
Please show this equality. n-1 p) p p-1-(1 p)"-1 p (1 -p) 7
Show proof of P(AUBUC) - P(A)+P(B) +PCC) - P(ANB) -P(BnC)-Planc) + P(AMBAC) use D to replace a use thm. P(AUB) = P(A)*P(B)- P(ANB)
Derive The Following Formulas (a) P(Ac)=1−P(A). (b) P(A∪B)=P(A)+P(B)−P(A∩B) (c) P(A ∩ B) = P(A|B)P(B) (d) E(aX + b) = aE(X) + b where you will be told whether X is assumed to be discrete or X is assumed to be continuous. (e) Var(X) = E(X2) − μ2 where you will be told whether X is assumed to be discrete or X is assumed to be continuous. (f) Var(aX + b) = a2Var(X)