6. Pick a uniformly chosen random point (X, Y ) inside a unit square [0, 1]×[0,...

6. Pick a uniformly chosen random point (X, Y ) inside a unit square [0, 1]×[0, 1], and let M = min(X, Y ). Find the probability that M < 0.3.

Expert Solution

orchestra answered 2 years ago

A point (a, b) is distributed uniformly in the square 0<x<1, 0<y<1. Let S(a, b) be...

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Let X and Y be uniformly distributed independent random variables on [0, 1]. a) Compute the...

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1. Let X and Y be independent U[0, 1] random variables, so that the point (X,...

1. Let X and Y be independent U[0, 1] random variables, so that the point (X, Y) is uniformly distributed in the unit square. Let T = X + Y. (a) Find P( 2Y < X ). (b). Find the CDF F(t) of T (for all real numbers t). HINT: For any number t, F(t) = P ( X <= t) is just the area of a part of the unit square. (c). Find the density f(t). REMARK: For a...

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Pick an arbitrary consumption bundle (x, y) ∈ R2+ (meaning x ≥ 0, y ≥ 0)....

Pick an arbitrary consumption bundle (x, y) ∈ R2+ (meaning x ≥ 0, y ≥ 0). Draw or describe the better than set (upper contour set), the worse than set (lower contour set) and the indifference set in a graph for the following situations: • I like consuming x, and the more the better. I am completely indifferent to the amount of y that I consume. • As long as my consumption of x is less than x∗, the more...

Let X and Y be uniform random variables on [0, 1]. If X and Y are...

Let X and Y be uniform random variables on [0, 1]. If X and Y are independent, find the probability distribution function of X + Y

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