Problem 3. Let X and Y be the discrete random variables with the given pmf px (x₁) and py (yi). Assume E[X²] < ∞, E[Y²] < ∞. Variance and covariance are defined as Var (X) = E[(X - E[X])²], Cov(X, Y) = E[(X – E[X])(Y — E[Y])]. Verify that ● Var(X) = E[X²] – E[X]². • Cov(X, Y) = E[XY] – E[X]E[Y]. • Var(aX + c) = a²Var(X). • Var (X + Y) = Var(X) + Var(Y) + Cov(X, Y).

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A: Solution Given   Y(t)=∫0tY(u)dW (u)+∫0tuduwe need to find the Y(t)?

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A: Solution

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A: It is an important part of statistics. It is widely used.

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A:

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A: @solution::::

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A: and  denote  random variables.The CDF: