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Recurrence Relation

Probability : Mean, Standard Deviation and Recurrence Relation

In order to test a vaccine, we have to find patients with a certain blood type, that is found in 20% of the population. Model W, the number of people sampled until we have found one with thhis blood type; X, the number sampled to find four with the blood type; and Y, the number with this blood type among 20 people. Find the mean

Domain and Range of a Relation

1. Find the domain and range of the relation {(x,y)&#9474;5x < -5} 2. Find the domain of the relation A={(x,y)&#9474;x^2+y^2=4}

Curls : Green's Theorem

When I write A_n it means A "sub" n. a) Define A_n= integral from 2pi to 0 of (Cos(theta))^(2n).d(theta) Proove the recurrence formula(*): A_n=(2n-1)/(2n)*A_(n-1) by writing Green's thorem for vector field F=x^(2n-1)j in the unit disc x^2+y^2<1 and evaluating each of the integrals sepa

Relations : Properties and Equivalence Classes

Please see the attached file for the fully formatted problem. Exercise 5 (4p) R is the relation defined on Z ts follows: for all m,n E Z, m R n <=>4|(m-n) a. Determine whether the relaition is reflexive. b. Determine whether the relation is symmetric. c. Determine whether the relation is transitive. d. In case the relat

Catalan Numbers

Prove recurrence relationship of Catalan Numbers. Question: Let n be a non-negative integer. The number, x[n], of topologically distinct binary trees with n nodes can be shown to satisfy the following recurrence (x[0] = 1): See attached file for full problem description.

Mathematical Induction

Prove that the Fibonacci sequence can be obtained by the recurrence relationship. See attached file for full problem description.

Fibonacci sequence in closed form

Prove that Fn can be expressed by: Fn=[(a^n-b^n)/(a-b)] for n=1,2,3... ~: Set Gn=[(a^n-b^n)/(a-b)] and show that Gn satisfies the recurrence formula {G(n+1) = Gn + G(n-1) for n=2,3,4...} and don't forget that a and b satisfy the equation x^2-x-1=0. a and b are the roots of x^2-x-1=0, which are (1+sqrt5)/2 and (1-sqrt5)/2

Discrete Structures

1. Consider the sequence of triangles Ti, i >= 2: T2 is simply a triangle sitting upright, on its base. T3 is T2, except that an additional straight line is drawn from the upper vertex, down to somewhere on the base. For each Ti+1, one more line is added to triangle Ti (such that each line meets the base at a different point).