Engineering

Engineering, 08.11.2019 19:31, cschellfamily

X, y , and z are three independent and uniformly distributed random variables be- tween zero and one. find the pdf of w = x + y + z. (hint: first find the pdf of v = x + y . the pdf of v should look like an isosceles triangle. then, find the pdf of w = v + z.)

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Mathematics, 13.08.2019 00:20, dathanboyd

Let x and y be independent continuous random variables that are uniformly distributed on (0,1). let h=(x+2)y. find the probability p(lnh≥z) where z is a given number that satisfies ez< 2. your answer should be a function of z.hint: condition on x.p(lnh≥z1)= ? let x be a standard normal random variable, and let fx(x) be its cdf. consider the random variable z=fx(x). find the pdf fz(z) of z. note that fz(z) takes values in (0,1) .fz(z)= ?

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Mathematics, 24.09.2019 09:30, fatty18

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

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Mathematics, 04.11.2019 21:31, sydneyyyy7014

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