(i) Show that if P(A) = 0 or P(A) = 1, then A is independent of every other event. Show that if A is independent of itself then P(A) is either O or 1. (ii) Suppose k events form a partition of the sample space N, i.e., they are disjoint and UL, A; = N. Assume that P(B) > 0. Prove that if P(A1|B) < P(A1), then P(A¡|B) > P(A¡) for some i = 2, ..., k.

Q: A cancer researcher wants to test a new combination of chemotherapy and radiation on skin tumors in…

A: Binomial distribution is used to when we have n number of independent trials and probability of…

Q: choose a number from the set {1, 2, 3, ..., 100} uniformly at random and denote this number by X.…

A: Given: 1, 2, 3, .........100 are there in a set. A number X is selected from above set. Independent…

Q: 2. If A and B are two events defined on the sample space Q, then P(A U B) ≤ P(A)+P(B) always. O TRUE…

A: If A and B are two events defined on tha sample space,then P(A U B)≤P(A)+P(B) Answer True

Q: #5 &amp; #6

A:

Q: Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P…

A: The given probabilities are:  and .

Q: Let F₁, F₂, and F3 are pairwise disjoint events from a sample space S - F₁F₂UF3. Let E be an event…

A: Given that F1, F2 and F3 are pairwise disjoint events from a sample space S=F1∪F2∪F3. E is an event…

Q: = Suppose k events for a partition of the sample space , i.e., they are disjoint and Ut_1 Ai P(A;)…

A:

Q: Conditon 1 P(W | Z)= P(Z | W) Condition 2 P(W) > P(Z)

A: Suppose A and B are two events defined on the same sample space. Then, the conditional probability…

Q: 1.) Let 2 be a deck of cards. Define a random variable X such that for any card e in the deck the…

A:

Q: The following two-way table shows the distribution of daily traffic and weather issues in a certain…

A: Given :

Q: 1. Let S represent the sample space. A and B are two events in the sample space, S. If S = {x | 2< x…

A: As per guideline expert have to answer first question only.

Q: Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P(A₁)…

A: The given probabilities are:  and .

Q: Suppose we have a sample space S and three events A, B, and C such that S = AUBUC and ANB= A and an…

A: To find p(E) :

Q: Consider the sample space (S, P) where S = {a,b,c} and P(a) = 0.4, P(b) = 0.4, and P(c) = 0.2. Let X…

A:

Q: 1.) Let 2 be a deck of cards. Define a random variable X such that for any card e in the deck the…

A: Let Ω be a deck of cards. Given that        X(e)= the number value on the card for all numbered…

Q: Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.7, Pr(B) = 0.5, Pr(C) = 0.2.

A: note -Hi! Thank you for the question, As per the honor code, we are allowed to answer three…

Q: Let S be a sample space and E and F are independent events associated with S. Suppose that Pr(E)=…

A: Solution

Q: Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P(A₁)…

A: It is given that, A1 and A2 are mutually exclusive events and form a complete partition of the…

Q: Let A and B be events in a sample space S such that P(A)= .4, P(B)= .5, and P(ANB) = .3. Find:…

A:

Q: Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.75, Pr(B) = 0.35, Pr(C) =…

A: Solution: From the given information, Pr(A)=0.75, Pr(B)=0.35 and Pr(C)=0.6.

Q: A doctor is called to see a sick child. The doctor has prior information that 95% of sick children…

A: Introduction: It is required to solve the question using Bayes' law.

Q: Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P(A₂)…

A: Given that A1 and A2 are mutually exclusive events..

Q: Events A₁ and A2 are mutually exclusive and form a complete partition of a sample space S with P…

A: Given that A1 and A2 are mutually exclusive events.P(A1)=0.48P(A2)= 1-P (A1) = 1-0.48 = 0.52P(E|A1)…