3. A certain market has both an express checkout line and a super-express checkout line. Let A denote the number of customers in line at the express checkout at a particular time of day, and let B denote the number of customers in line at the super-express checkout at the same time. Suppose the joint PMF of A and B is as given in the following table. B 1 2 3 A 0.08 0.07 0.04 1 0.06 0.15 0.05 0.04 2 0.05 0.04 0.1 0.06 3 0.03 0.04 0.07 4 0.01 0.05 0.06 a. What is P(A = B), that is, the probability that the numbers of customers in the two lines are identical? b. What is the probability that the total number of customers in the two lines is exactly four? At least four? c. Determine the marginal PMF of A and B and then calculate the expected number of customers in line at the express checkout. d. If ata given time there are 3 customers in line at the express checkout, what is the probability of 2 customers being in line at the super-express checkout? e. By inspection of the probabilities P(A = 4), P(B = 0), and P(A = 4, B = 0), are A and B independent random variables? Explain.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
donumber c, d, e
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