Let E, and E, be events with IP(E1) > 0 and P(E2) > 0. Prove that if P(E, E2) > P(E1) then P(E2|E1) > P(E2

Q: Prove - If X and Y are independent random variables, then E(XY ) = E(X)E(Y ). (You can assume that…

A: Assume that X and Y are two independent discrete random variables.

Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…

A: We use the conditional probability formula to prove that A and B are independent.…

Q: Assume that events A and B are independent, and C ⊂ A, and C ⊂ B. Moreover, P(A) = 1/2, P(B) = 2/3,…

A:

Q: 3. A and B are events such that P(A) = 0.2 and P(A U B) = 0.5. Find P(B) in each of the following…

A: There are two events A and B are given.The given probabilities are as follows

Q: Let A and B be two events with 0 P(B | A). Verify that P(A) > P(B) b.) Suppose that P(A | B) >…

A: a)  Given that P(A|B) &gt; P(B|A)or, P(A∩B)P(B)&gt;P(A∩B)P(A)or, 1P(B)&gt;1P(A) [cancel P(A∩B) from…

Q: Suppose that  A  and  B  are independent events such that  =PA0.10  and  =PB0.70 . Find  P∩AB  and…

A: From the provided information,P (A) = 0.10P (B) = 0.70The events A and B are independent.

Q: If E and F are independent events with P(E) = 0.33 and P(F) = 0.33, then what is P(EC U U F)?

A: If E and F are independent events, then P(Ec∩F) = P(Ec)*P(F), where P(Ec) =[1 - P(E)] P(Ec∪F) =…

Q: A and B are independent events. If Pr[A]=0.5 and Pr[B]=0.7, what is Pr[A∩B′]?

A:

Q: Let E and F be two events in S with P(E) = 0.39, P(F) = 0.4, and P(E ∩ F) = 0.22. Find P(EC ∩ F) and…

A: To compute the probabilities of the required events , using addition and complementation laws

Q: Suppose that X and Y are discrete random variables on the probability space (Q.F.P). Show that E[aX]…

A: The objective of this question is to prove two properties of the expected value (E) of random…

Q: Let A and B be independent events with P(A) = P(An B) = P(AUB) = 1 ·|6 1 and P(B) = Find P(An B) and…

A:

Q: Q2. Two events A and B are said to be dependent if and only if:

A: Here use basic of dependent events

Q: Let A and B be events such that P(A)=1/4, P(A or B)=1/3, and P(A and B)=1/5. DetermineP(B)

A:

Q: For any two disjoint events E and F. P(EUF) = P(E) + P(F) Select one: O True O False

A: For any two disjoint events E and F.

Q: Let E and F be two events in S with P(E) = 0.45, P(F) = 0.63, and P(E ∪ F) = 0.87. Find P(E ∩ F) and…

A: Formula:For 2 events A and B, P (A ⋃ B) = P (A) + P (B) – P (A ∩ B).

Q: Let E and F be independent events such that P(E) = 0.4, P(F) = 0.6.. Find P(E| F) and P(E U F). 5.

A:

Q: If P(E) = 0.2, P(F) = 0.3, and E and F are independent events, find P(E and F). 1) 0.06 2) 0.08 3)…

A: P(E)=0.2P(F)=0.3and E,F are independent events.

Q: Let E and F be two events in S with P(E) = 0.62, P(F) = 0.49, and P(En F) = 0.39. Find P(En F) and…

A: P(E) = 0.62 P(F) = 0.49 P(E∩F) = 0.39

Q: Suppose that E and F are two events and that P(E)=0.8 and P(F|E)=0.5. What is P(E and F)​?

A: Given data,  P(E)=0.8  P(F|E)=0.5 P(E and F)​=?

Q: Let E1 and E2 be events with P(E1)>0 and P(E2)>0. Prove that if P(E1|E2)>P(E1) then P(E2|E1)>P(E2)

A:

Q: A and B are independent events. If Pr[A]=0.3 and Pr[B]=0.7, what is Pr[A∩B′]?

A: From the provided information,

Q: Let A and B be events such that​ Pr[A] =0.370.37​, Pr[B] =0.630.63​, and​  Pr[A ∩​ B] =0.240.24.…

A: Required to calculate the conditional probability that A occurs given B has occured, P(A|B)

Q: Let A and B be events such that​ Pr[A] = 0.43​, ​Pr[B] = 0.54​, and​ Pr[A ∩​ B] = 0.23. Find ​…

A: