Find the probability that a mole of aroma particles develop from their open 100 ml diffuser into an environment of 1 L volume (like a deskspace). Expecting your numerical result isn't unclear, track down the nearest number planning with your result.

Social occasion of answer choices

100 x (1 mole)

10^(1.381x10^-23)

10^(1 mole)

100%

~23~

Top Fruit Distributing understands that all through the past four years, the mean (or typical) time it takes a particular truck to get all over town has been 6.32 hours with standard deviation 0.41 hours.

(a) Suppose you mean to see this truck on numerous occasions. What is the vague transport of the subjective model interim? Similarly decide its limits.

A gathering association uses two devices to explore yield for quality control purposes. The essential device can accurately perceive 99.3% of the defective things it gets, however the second can das such in 99.7% of the cases. Acknowledge that four harmed things are conveyed constantly for assessment. Permit X and Y to connote the amount of things that will be perceived as defective by exploring devices 1 and 2, separately. Acknowledge that the devices are self-governing.

A.) Determine fxy(X=4,Y=3).

B.) Determine fxy(X=3,Y=4)

C.) Determine fxy(X=4,Y=4)

D.) Determine fxy(X=4)

A paper sack contains three dice. Dice An's appearances are numbered 1, 2, 3, 4, 5, 6; Dice B's faces are numbered 2, 2, 4, 6, 6,

additionally, 6; and Dice C has every one of the six appearances numbered 6. You draw dice from the sack and move it twice. What is the probability

that you get 6 the on various occasions?

Problem 2. (20 pts.) Suppose that the log-ons to a computer network follow a Poisson process with an average of 0.1 counts per minute. 1. What is the probability that three counts in an hour? 2. What is the mean time between consecutive counts? 3. What is the variance between four counts in a row? 4. Determine t such that the probability that at least one count occurs before time t minutes is 0.975. 2} Starting from the tines axioms of probability given on slide 10 of presentation \"Overview of Probability Theory 3: Statistics and repeated hereafter for completeness, prove Theorems 1] to 1-? on slides ll 3: 12 of the same presentation, Axioms of Probability- Suppose we have a sample space S. If S is discrete, all subsets correspond to events and conversely; if S is not discrete, only special subsets {called measurabie) correspond to events. To each event A in the class C\" of events, we associate a real number Pm)- The P is called a probability mctim and P134} the probability of the event, if the following axioms are satised. Axiom 1: For every eventA in class (3', HA} 3 Axiom 2: For the sure or certain event 3 in the class C, HS} = l Axiom 3: For any number of mutually exclusive events {synonymous with disjoint) A], A1, in the class C. FLA. UA1U )=P(A1}+P(A2)+ You can also employ the following definitions of Set Theory: - The empty set, {L is the unique set having no elements; its size or cardinality {count of elements in a set) is zero. - If all the members of set A are also members of set B, then A is a subset of B, denoted A E B. - Union of the sets A and B, denoted A U B, is the set of all objects that are a member of A, or B, or both. - Intersection of the sets A and B, denoted A H B, is the set of all objects that are members of both A and B. - Set difference of U and A, denoted U - A, is the set of all members of U that are not members of A. Also, when A is a subset of U, the set difference U A is also called the complement of A in U, A'. Problem 2. Throughout this problem, A and B are events and 2 is some sample space. There are three axioms of probability. From these, in class, we deduced: . P(0) = 0. . Finite additivety: P(U._Ai) = EP(A;) when Al, ..., An are mutually ex- clusive. . P(Ac) = 1 - P(A). Using the axioms and any of the above consequences, show: (1) A C B implies P( A)