(ii) The events Pand Q are such that P(P) =, P(PnQ) = and P(P]Ø)= ;. Find (c) P(Q), (d) P(Q|P), (e) determine whether the events P and Q are independent.

Q: Find P(A and B) if P(A) is 0.3 and the P(B) is 0.4, and events A and B are independent.

A:

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

Q: If A and B are events such that ​P(A)equals=0.60 and P(A∪​B)equals=0.70​, find​ P(B) when ​(a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: - Let X1,.. Xn is a random sample from Binomial(p1) and Y,.., Ym is another independent random…

A:

Q: Suppose that F and X are events from a common sample space with P(F) # 0 and P(X) #0. Prove that PX)…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: A computer-consulting firm presently has bids out on two projects. Let A= [awarded project 1] and B=…

A: Given: PA=0.75, PB=0.35 and PA∩B=0.2.

Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.

A: Proof: PA=PA∩A=PAPA  Since A is independent itself.⇒PA1-PA=0PA=1  Since P(A)>0

Q: Example 2.3.11 Show that for any two events A and B, P(AN B) s P(A) s P(A U B) s P(A) + P(B) nned…

A:

Q: Suppose for this random variable X we want to compute P(X ≤ 3)

A:

Q: The PMF of the number N of customers that arrive at a local li- brary within a one-hour interval is…

A: Solution

Q: Prove or disprove that for any two events A, and A2, P[A, n A-] 21- PÍAG] – P[A£]

A:

Q: If A and B are independent events such that P(A) = 0.4 and P %3D

A: Concept: If the probability of occurrence of one event is not affected by the probability of…

Q: The P(A)=0.48P(A)=0.48 and the P(B)=0.06P(B)=0.06. Events AA and BB are mutually exclusive. What is…

A: Given, P(A)=0.48 P(B)=0.06 P(A or B)=?

Q: assume that Pr[A∪B]=0.6 and Pr[A]=0.2 (1) What is Pr[B] if A and B are independent events?

A: Since A and B are independent event, so pr(A∩B)= pr(A)pr(B).

Q: A certain market has both an express checkout line and a superexpress checkout line. Let X1denote…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

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

A: Given, Pr(A) = 0.5 Pr(B) = 0.5 To calculate PrA∩B'

Q: Theorem 3.16. For any three events A, B and C, Р (AnB IC)+ P (AnBIC)- Р (AI C)

A:

Q: Q1: If the event A is independent with itself, then P(A) is

A: The statement is the event A is independent itself.

Q: Since events A and B are independent events; Prove that the events depicted in the picture are…

A: Given that the events A and B are independent events.

Q: From a standard deck of 52 playing cards, two cards are drawn in succession and at random without…

A: There are 52 cards in a standard deck. The number of ways 2 cards can be selected without…

Q: Suppose that X and Y are independent normal random variables and - XE N(6,1) Y € N(8, 2) Find P(X -…

A: We have given that , X€N(6,1)       Y€(8,2) . We have to find, P(X-Y>0) = ?

Q: Suppose an insect lays a very large number of eggs Y, where Y ~ Po(lambda), and suppose that each…

A: Introduction: The random variable Y denotes the number of eggs laid by a randomly chosen insect. It…

Q: Suppose that A and B are events such that P(A) = 2/7 and P(A&B) = 3/25. Determine P(B| A).

A:

Q: Suppose that A and B are events such that P (A|B) = P (B|A) , P(AUB) = 1, and P(An B) > 0. Prove…

A: Solution: From the given information,

Q: a. What is P(Xi= 1, X2= 1), that is, the probability that there is exactly one customer in each…

A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   Given :

Q: If we let kσ = c in Chebyshev’s theorem, what doesthis theorem assert about the probability that a…

A:

Q: Suppose the following Question expression is given: P(X5=3|X4=3,X3=3,X2=1,X1-4, X0=1). a) Write down…

A: This problem is based on the markovian property. Markovian property says that future is independent…

Q: Suppose that C and D are independent events such that P(C) = 0.7 and P(D) = 0.6. Find (C&D).

A: Two events C and D are said to be independent if,

Q: Compute the probability of each of the following events (i) X <1 1/2 (ii) XY is even

A:

Q: When two events cannot occur at the same time, they are said to be OA mutually exclusive. OB. not…

A: In this case, we need to find the suitable option for the given statement.

Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…

A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3

Q: A sample of n=16 scores is selected froma normal population with μ=56 and σ=20. What is the…

A: Given that, A sample of n=16 scores is selected from a normal population with μ=56 and σ=20.

Q: Let X and Y be two independent random variables distributed uniformly on the interval [0, 1]. What…

A:

Q: A and B are independent events. If Pr(A n B) = 0.16 and Pr[A] = 0.2 what is Pr[B]?

A: If A and B are two independent events then:

Q: Two numbers x and y are selected at random between 0 and 1. Let the events A, B and C be defined as…

A: A = {x &gt; 1/3} B = {y &gt; 2/3} C = {x &gt; y} (x, y) ∈ (0, 1)

Q: I toss a fair die twice, and obtain two numbers X and Y. Let A be the event that X=2, B be the event…

A: A fair dice have 6 faces 1, 2, 3, 4, 5 and 6 and let X and Y be the two numbers obtained in a toss.

Q: If P (Event A)=0.2 and P(Event B)=0.3, and the two events are disjoint, then P (Event A and Event B)…

A: Disjoint events : if two events A and B are disjointevents then the two events can not occure at the…

Q: AA and BB are independent events. If Pr[A]=0.3Pr[A]=0.3 and Pr[B]=0.5Pr[B]=0.5, what is…

A:

Q: Let A and B be two events such that P(AC) = 0.70, P(B) = 0.50, and P(A U B) = 0.60. What is P(An B)?

A:

Q: A pharmaceutical company has developed a new drug to help relieve acid reflux. However, as with all…

A: Let's take n = 4000, k = 9, thus: Proportion of drug takers who will experience adverse side effects…

Q: Suppose that A, B and C are three independent events such that P(A)=0.2, P(B)=0.5 and P(C)=0.1.…

A:

Q: Consider the following two events for a randomly selected adult: Y = N = this adult has shopped on…

A:

Q: IJ A and B are independent events, prove that the events A and B, A and B; and A and B are also…

A: Answer: For the given data,

Q: d) What is the probability that a random element of Zy is not in Z,? e) Do you think there can be an…

A: d) Write φn=2em with m odd and e≥1. Then the probability that a random element of ℤn is not in ℤn*…

Q: 6. Imagine that a zealous prosecutor (P) has accused a defendant (D) of com- mitting a crime.…

A: *Answer:  *a

Q: 1. Given that x is a continuous random variable that is uniformly distributed in a range from 8 to…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: The odds against a certain event are 5 to 2 and the odds in favour of another (independent) event…

A: Odds is defined as the prob. of occurrence of an event divided by the prob. that the event will not…

Q: Which pair(s) of events are Mutually Exclusive.

A: In a competition, two people will be selected from four finalists to receive first prize and second…

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!