Let X and Y be two independent samples of a standard uniform distri- bution. Let Z...

Let X and Y be two independent samples of a standard uniform distri- bution. Let Z be the closest integer to X/Y (i.e. the value that we get by rounding X/Y ). Is Z more likely to be even or odd? (hint: draw the sample space over X and Y and identify the regions where Z is even or odd. Work out when Z = 0, when Z = 1, and so forth)

Expert Solution

orchestra answered 2 years ago

Let X and Y be independent and identical uniform distribution on [0, 1]. Let Z=min(X, Y)....

Let X and Y be independent and identical uniform distribution on [0, 1]. Let Z=min(X, Y). Find E[Y-Z]. Hint: condition on whether Y=Z or not. What is the probability Y=Z?

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...

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Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?

Let X and Z be two independently distributed standard normal random variables and let Y=X2+Z. iShow...

Let X and Z be two independently distributed standard normal random variables and let Y=X2+Z. iShow thatE(Y|X) =X2 iiShow thatμY= 1 iiiShow thatE(XY) = 0ivShow that cov(X,Y) = 0 and thus ρX,Y= 0

The curried version of let f (x,y,z) = (x,(y,z)) is let f (x,(y,z)) = (x,(y,z)) Just...

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Let X,,X, and X, be independent uniform random variables on [0,1] Write Y = X, +X,...

Let X,,X, and X, be independent uniform random variables on [0,1] Write Y = X, +X, and Z = X+ X. a.) Compute E[X,X,X,. (5 points) b.) Compute Var(X). (5 points) c.) Compute and draw a graph of the density function fr. (15 points)

Let X and Y be independent positive random variables. Let Z=X/Y. In what follows, all occurrences...

Let X and Y be independent positive random variables. Let Z=X/Y. In what follows, all occurrences of x, y, z are assumed to be positive numbers. Suppose that X and Y are discrete, with known PMFs, pX and pY. Then, pZ|Y(z|y)=pX(?). What is the argument in the place of the question mark? Suppose that X and Y are continuous, with known PDFs, fX and fY. Provide a formula, analogous to the one in part (a), for fZ|Y(z|y) in terms...

Let X and Y be two independent random variables such that X + Y has the...

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

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