An important thing to understand is the following set of statements: “if random variables x and y are independent, they are uncorrelated. if random variables x and y are uncorrelated and jointly gaussian, they are independent.” this problem gently walks you through the nuances of this thinking. (a) often, a counterexample to an intuitive rule is some pathological case. however, this example occurs in standard communication systems; your cell phone is generating these random variables right now. let θ be a continuous random variable uniformly distributed on [0, 2π]. let x = cos θ and y = sin θ. show that, for this x and y , x and y are uncorrelated but not independent. (hint: as part of the solution, you will need to find e[x], e[y ] and e[xy ]. this should be pretty easy; if you find yourself trying to find fx(x) or fy (y), you are doing this the (very) hard way.) (b) (note: this part is ridiculously easy and i know that you saw it in lecture, but i give it to you so that you will hopefully remember it.) recall that two random variables x a

la parábola es el lugar

geométrico en el cual los puntos tienen una distancia idéntica, equidistantes,

de un punto denominado foco, f, y una recta denominada directriz

el radio vector de una

parábola es el segmento que existe entre un punto cualquiera y el foco.

por la ecuación se observa

que la parábola abre hacia la derecha, por lo cual podemos usar las siguientes fórmulas

la ecuación ordinaria de la

parábola es y^2 = 4px, donde p es la longitud desde el vértice de la parábola al

foco.

la fórmula de la directriz

es x + p = 0

resolviendo:

y^2-9x = 0

y^2 = 9x

4p = 9, entonces p = 9/4

entonces el foco tendrá la

coordenada f(9/4,0)

la directriz vendrá

expresada por

x + p = 0

x = -p

x = -9/4

el problema indica que la

ordenada es igual a 6, entonces

(6)^2=9x

x = 36/9

x = 4

entonces el punto al cual

hay que obtener la distancia será p(4,6)

calculando se tendrá: pf = 

pf = 6,25 u

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step-by-step explanation:

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%

step-by-step explanation:

step-by-step explanation:

a'(12.5,11.25)

slope=(y1-y2)/(x1-x2)