3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative a procedure with considerable HIV risk. Although this practice is common, little is known about the prevalence of such practices. The researchers asked injection drug users in four neighborhoods in the South Bronx if they ever "got down on" drugs in bags or shots. The results classified by gender and splitting practice are given below: Gender Split Drugs Never Split Drugs Total WeITIMINO Male 349 324 673 Female 220 128 348 Total 569 452 1021 Source: Daniel Fernando, Robert F. Schilling, Jorge Fontdevila, and Nabila El-Bassel, "Predictors of Sharing Drugs among Injection Drug Users in the South Bronx: Implications for HIV Transmission," Journal of Psychoactive Drugs, 35 (2003), 227-236. toe (a) How many marginal probabilities can be calculated from these data? State each in probability notation and do the calculations. (b) How many joint probabilities can be calculated? State each in probability notation and do the calculations. (c) How many conditional probabilities can be calculated? State each in probability nota- tion and do the calculations. (d) Use the multiplication rule to find the probability that a person picked at random never split drugs and is female. (e) What do we call the probability calculated in part d? (f) Use the multiplication rule to find the probability that a person picked at random is male, given that he admits to splitting drugs. (g) What do we call the probability calculated in part f? Refer to the data in Exercise 3.4.2. State the following probabilities in words and calculate: (a) P(Male n Split Drugs) (b) P(Male U Split Drugs) (c) P(Male|Split Drugs) (d) P(Male) qu? 3.4.3 3.4.4 If the probability of left-handedness in a certain group of people is .05, what is the prob- ability of right-handedness (assuming no ambidexterity)? The probability is .6 that a patient selected at random from the current residents of a certain 3.4.5 hospital will be a male. The probability that the patient will be a male who is in for surgery is .2. A patient randomly selected from current residents is found to be a male; what is the probability that the patient is in the hospital for surgery?
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.
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