Ch5 Study Questions File
... a) What is the probability of a tip of $200 or more? b) Are the categories “$0 up to $20” , “$20 up to $50” and so on considered mutually exclusive? ...
... a) What is the probability of a tip of $200 or more? b) Are the categories “$0 up to $20” , “$20 up to $50” and so on considered mutually exclusive? ...
Introduction to Probability Exercise sheet 3 Exercise 1. 5 cards
... Exercise sheet 3 Exercise 1. 5 cards labelled 10, J, Q, K, A are ordered randomly, all orders equally likely. What is the probability that A is first and K is fourth, conditioned on Q being third? Exercise 2. In Eurasia 10% of males are illiterate, and 5% of females are illiterate. The population co ...
... Exercise sheet 3 Exercise 1. 5 cards labelled 10, J, Q, K, A are ordered randomly, all orders equally likely. What is the probability that A is first and K is fourth, conditioned on Q being third? Exercise 2. In Eurasia 10% of males are illiterate, and 5% of females are illiterate. The population co ...
COMP 245 Statistics Exercises 2
... P(E ∪ F) = P(E) + P(F) − P(E ∩ F). 2. Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. 3. What is the probability that a single roll of a die will give an odd number if (a) no other information is given; (b) you are told that t ...
... P(E ∪ F) = P(E) + P(F) − P(E ∩ F). 2. Suppose two events E and F are mutually exclusive. State the precise conditions under which they may also be independent. 3. What is the probability that a single roll of a die will give an odd number if (a) no other information is given; (b) you are told that t ...
Statistics 3
... In the MEI Structured Mathematics specification, no calculator is allowed in the examination for C1. For all other units, including this one, a graphical calculator is allowed. ...
... In the MEI Structured Mathematics specification, no calculator is allowed in the examination for C1. For all other units, including this one, a graphical calculator is allowed. ...
Lecture 14 - Stony Brook AMS
... values A. For the invertible function h: AR, let Y=h(X) be a random variable with the set of possible values B=h(A)={h(a):aA}. Suppose that the inverse of y=h(x) is the function x=h-1(y), which is differentiable for all value of yB. Then fY, the density function of Y, is given by f Y ( y) f X ( ...
... values A. For the invertible function h: AR, let Y=h(X) be a random variable with the set of possible values B=h(A)={h(a):aA}. Suppose that the inverse of y=h(x) is the function x=h-1(y), which is differentiable for all value of yB. Then fY, the density function of Y, is given by f Y ( y) f X ( ...
Assignment 8
... (marginal) probability density functions of each of the three arrival times S1 , S2 , S3 . 3. Customers arrive at a facility according to a Poisson process {N (t) : t ≥ 0} of rate λ, with arrival times S1 , S2 , . . .. Each customer pays $1 on arrival. At time t, the discounted value of the total PN ...
... (marginal) probability density functions of each of the three arrival times S1 , S2 , S3 . 3. Customers arrive at a facility according to a Poisson process {N (t) : t ≥ 0} of rate λ, with arrival times S1 , S2 , . . .. Each customer pays $1 on arrival. At time t, the discounted value of the total PN ...
Probability box
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A probability box (or p-box) is a characterization of an uncertain number consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modeling where numerical calculations must be performed. Probability bounds analysis is used to make arithmetic and logical calculations with p-boxes.An example p-box is shown in the figure at right for an uncertain number x consisting of a left (upper) bound and a right (lower) bound on the probability distribution for x. The bounds are coincident for values of x below 0 and above 24. The bounds may have almost any shapes, including step functions, so long as they are monotonically increasing and do not cross each other. A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.