mustache and beard and also drove a yellow car. Based on this evidenCE THE PUNCO alTUJIu Because there were no eyewitnesses and no real evidence, the prosecution used probability to make its case against the defendants. The probabilities listed below were presented by the prosecution for the known characteristics of the thieves. Characteristic Probability Yellow car 1/10 Man with mustache 1/4 Woman with ponytail 1/10 Woman with blonde hair 1/3 Man with beard 1/10 Interracial couple in a car 1/1000 (a) Assuming that the characteristics listed above are independent of each other, what is the probabilit a randomly selected couple has all these characteristics? That is what is, calculate the probability: P( "yellow car" and "man w/ mustache, beard and ... "interracial couple in car") (b) Based on the above result would you convict the defendant? Explain thoroughly. ) Now let n represent the number of couples in the Los Angeles area who could have committed the (c) crime. Let p represent the probability that a randomly selected couple has all 6 characteristics listed in the table. Assuming that the random variable X follows the binomial probability function, we have: P(X) = C(n,x) ' P* (1-p)"-x, x 0, 1, 2, ...n %3D Note: Use the calculator link http://stattrek.com/online-calculator/binomialaspx Assuming there are n 50,000 couples in the Los Angeles area, what is the probability that more than one of them has the characteristics listed in the table? %3D P(X > 1) = (d) Does this result cause you to change your mind regarding the defendant's guilt? Explain. (e) The probability that more than one couple has these characteristics assuming there is at least one couple is given by the formula below and each is evaluated with the binomial formula from (c). P(X >1 |X > 1) = P(X > 1) %3D %3D P(X 21) (f) Do you think the couple should be convicted "beyond all reasonable doubt" based on the answer fror part (e)? Explain why or why not.
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.
According to the graph part c,d,e, and f
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