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In: Statistics and Probability

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1.

  1. Find the value of k that makes this a probability density function.
  2. Compute the probability that P(X≤3/4, Y≥1/2).
  3. Find E(X).
  4. Find E(X|Y=y).

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