Let $X \sim U(0, 1)$ and $Y \sim U(0, 2)$ be independent random variables. Find $\mathbb{E}[|X - Y|]$. I found $f_{X}(x) = 1$ and $f_{Y}(y) = 1/2$, and I ...

Could someone explain what does it mean by "(and hence $\sum a_n$)"? Isn't $a_{n+1} \leq a_n$ for all $n$? How does the convergence of $\sum a_{n+1}$...

First off, I don't think this is a duplicate. Sorry if it is! Second this is not a homework question, so completeness is much appreciated. I am tryin...

Why must the following condition be satisfied before we can use Green's Theorem: L and M are functions of (x, y) defined on an open region containing...

I need help in finding maximal solution for the problem: $$ \cases {{\dot{x} = x^2+t}\\{x(0)=0}}$$ I know that because $x(1) \geq \frac{1}{2}$ and that ev...

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Are they the same thing just named differently or with minor differences?

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