Consider the probability triple [0, 1]2, B[0, 1], Leb2), where Leb2 is the two dimensional Lebesgue measure on [0, 1]2. You may use the fact that for A [0, 1]2, Leb₂ (A) is given by the area of the set A. Let X: [0, 1]2 → R and Y[0, 1]2 → R be random variables defined by X(W₁, W₂) = W₁ + W₂₂ Y(W₁, W₂) = W₂ - W1. w2) Let Fx,y be the joint cumulative distribution function of X and Y with respect to the two dimensional Lebesgue measure. Find Fx,y (0.9,0.09). Give your answer in four decimal places. Answer:

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Consider the probability triple [0, 1]?, B[0, 1],Leb, ), where Leb, is the two
dimensional Lebesgue measure on [0, 1]². You may use the fact that for
AC [0, 1]², Leb2(A) is given by the area of the set A.
Let X : [0, 1]2 →→ R and Y[0, 1]² –→ R be random variables defined by
X(w1, w2) = w1 + w2,
Y(w1, W2) = w2 - W .
Let Fxy be the joint cumulative distribution function of X and Y with respect to the
W2 –
two dimensional Lebesgue measure.
Find Fx.Y (0.9,0.09). Give your answer in four decimal places.
Answer:
Transcribed Image Text:Consider the probability triple [0, 1]?, B[0, 1],Leb, ), where Leb, is the two dimensional Lebesgue measure on [0, 1]². You may use the fact that for AC [0, 1]², Leb2(A) is given by the area of the set A. Let X : [0, 1]2 →→ R and Y[0, 1]² –→ R be random variables defined by X(w1, w2) = w1 + w2, Y(w1, W2) = w2 - W . Let Fxy be the joint cumulative distribution function of X and Y with respect to the W2 – two dimensional Lebesgue measure. Find Fx.Y (0.9,0.09). Give your answer in four decimal places. Answer:
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