Probability mass function: mean, variance, standard deviation

2.) Suppose X has probability mass function Pr{X = k} = c(k + 2) for k = -1, 0, 1, 2 . Find c, and compute the mean, variance, and standard deviation of X. Let Y = 3X + 5. Compute the mean, variance and standard deviation of Y

Probability density function

3.) Suppose X has probability density function f(s) = c(1 + s) for -1 <= s <= 1. Determine c and the mean, variance, and standard deviation of X. Let Y = 3X + 5. compute the mean, variance, and standard deviation of Y.

Vector analysis

Apply Green's Theorem to evaluate the integral over C of 2(x^2+y^2)dx + (x+y)^2 dy, where C is the boundary of the triangle with vertices (1,1), (2,2) and (1,3) oriented in the counterclockwise direction. Also check the result by direct integration. Please show detailed working so I can follow the steps of the working. ...continues

Real Analysis : Integrability

Prove that if f : [a,b] ----> R is a bounded function that is continuous at all but finitely many points, then f is integrable over [a,b].

Number Patterns : Door Problem

A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one. A second student then closed every second one (#2, 4, 6, 8 etc). A third student then changed every third locker (#3, ...continues

Probabilty of Hearing a Song in a Movie if it is Turned on at Random

What is the probability of hearing the song Moon River play from the top in the movie Breakfast at Tiffany's the moment the television set is turned on at random? This is a probability problem: An event happened to me which I label as "synchronicitic" but I want to determine what the probability that this particular event ...continues

Functions: Mapping

For the functions f defined below, determine which are 1:1, onto or both. 1) f: R onto R, f(x) = |x| 2) f: R onto R, f(x) = x^2 + 3 3) f: R onto R, f(x) = x^3 + 3 4) f: R onto R, f(x) = x(x^2-4) 5) f: R onto R, f(x) = |x| + x 6) f: N onto N, f(x) = x + 1 7) f: N onto NxN, f(x) = (x,x) 8) f: NxN onto N, f( ...continues

Symbolic Logic Problem

I have to determine whether or not this formal argument below is valid. If it is I have to provide a derivation of the conclusion from the premises, which I don't know how to do. If it is invalid, an interpretation which shows the invalidity must be constructed. The & signs mean "and" usually signified by a dot. The asterisk ...continues

Symbolic Logic Problem

I need to know how to construct a formal proof which shows that the sentence below is a theorem of predicate logic. The ^ sign indicates the word "or". The asterics indicates a conditional usually indicated by an arrow. No quantifier negation rules can be used. [(X)(~RX^NX)&~(EX)NX^(EY)(Z)SZY] * (~(EX)RX ^ (Z)(EY)SZY)

Symbolic Logic : Predicate Logic

The asterisk implies a conditional usually indicated by an arrow. The & sign indicates "and". In Aristotelian logic (X)(FX*GX) logically implies (EX)(FX & GX). Is this true in predicate logic? If not, why not?