(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that
P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1).
(b) Let A and B1 be independent; similarly, let A and B2 be independent. Show that in this case, A and B1∪B2 are independent if and only if A and B1∩B2 are independent.
(c) Given P(A) = 0.42,P(B) = 0.25, and P(A∩B) = 0.17, find
(i)P(A∪B) ;
(ii)P(A∩Bc) ;
(iii)P(Ac∩Bc) ;
(iv)P(Ac|Bc).
Complete solution is given in attached images:
Thank You.
(a) Let P(B1∩B2)>0, and A1∪A2⊂B1∩B2. Then show that P(A1|B1).P(A2|B2)=P(A1|B2).P(A2|B1). (b) Let A and B1 be independent;...
2. (a) Let P(Bin B2) > 0, and AUA, CBin B2. Then show that P(A/B).P (A2|B2) = P(A|B2).P (A2|Bi). (b) Let A and Bbe independent; similarly, let A and B, be independent. Show that in this case, A and B U B2 are independent if and only if A and Bin B2 are independent (c) Given P(A) = 0.42, P(B) = 0.25, and P(An B) = 0.17, find (i) P (AUB); (ii) P(An B°); (iii) P(A n B); (iv) P(...
GAME 3 Player B B1 B2 Player A A1 7,3 5, 10 A2 3,8 9,6 In Game 3 above, if the players move sequentially with Player B choosing first, the Nash equilibrium will be a) Player A choosing A2 and Player B choosing B1 b) Player A choosing A2 and Player B choosing B2 c) Player A choosing A1 and Player B choosing B2 d) Player A choosing A1 and Player B choosing B1
Given these probabilities, complete the contingency table, and compute the following probabilities: a) P(A2 and B1) b) P(A1 | B1) c) P(B2 | A2) d) P(B2 or A1) A1 A2 Total B1 0.56 B2 Total 0.46
given the following joint probability table A1 A2 B1 .02 .01 B2 .05 .02 Calculate the conditional probability P(A1IB1) round your answer
float useless(A){ n = A.length; if (n==1) { return A[@]; let A1,A2 be arrays of size n/2 for (i=0; i <= (n/2)-1; i++){ A1[i] = A[i]; A2[i] = A[n/2 + i]; for (i=0; i<=(n/2)-1; i++){ for (j=i+1; j<= (n/2)-1; j++){ if (A1[i] == A2[j]) A2[j] = 0; b1 = useless(A1); b2 = useless (A2); return max(b1,b2); What is the asymptotic upper bound of the code above?
(14) Show that if [(a1,b)- [(a2, b2) and [c,d) (c2, d2)] and bidi(aidi -b)>0 then b2d2(azd2 - b2c2) > 0. (This was the proposition which allows us to know that > on Q is well-defined. ) (14) Show that if [(a1,b)- [(a2, b2) and [c,d) (c2, d2)] and bidi(aidi -b)>0 then b2d2(azd2 - b2c2) > 0. (This was the proposition which allows us to know that > on Q is well-defined. )
Urgent!! Please show mark all correct answers and also find values of a1,a2,a3,a4,a5,a6 and b1,b2,b3,b4,b5,b6. Thank you! (1 point) The second order equation x?y" + xy' +(x2 - y = 0 has a regular singular point at x = 0, and therefore has a series solution y(x) = Σ CGxhtr P=0 The recurrence relation for the coefficients can be written in the form of n = 2, 3, ... C =( Jan-2 (The answer is a function of n and...
1. Prove“inclusion-exclusion,”thatP(A∪B)=P(A)+P(B)−P(A∩B). 2. Prove the “unionbound, ”thatP(A1∪A2)≤P(A1)+P(A2). Under what conditions does the equality hold? 3. Provethat, for A1 andA2 disjoint, P(A1∪A2|B)=P(A1|B)+P(A2|B). 4. A and B are independent events with nonzero probability. Prove whether or not A and Bc are independent.
Urgent!! Please label all the answers and find a1,a2,a3 and b1,b2,b3. (1 point) The second order equation x2y" - (x – ķ) y = 0 has a regular singular point at x = 0, and therefore has a series solutio y(x) = Σ CnN+r n=0 The recurrence relation for the coefficients can be written in the form Cn =( DCn-1, n = 1,2, ..., (The answer is a function of n and r.) The general solution can be written in...
6. Consider two possible networks for connecting points X and Y: a1 bi Л. C) b2 a2 Network 1 Network 2 and let A : Event that switch ai įs closed. A2Event that switch a2 is closed. Bi : Event that switch bi s closed B2 Event that switch b is closed We are given that P(A) = 0.8,P(A2) = 0.8, and that the events A1 and A2 are independent. Similarly, we are given that P(B) = 0.9. P(B) =...