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I've tried to attempt all these questions myself first but could someone tell me if these are correct?

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NookLines
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1 Answers1

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The first is okay.   You have found $f_Y(y)$, and $f_X(x)$, although you should also make note of their supports.

The second is not okay.   You are after: $f_{Y\mid X}(y\mid x) ~=~ \dfrac{f_{X,Y}(x,y)}{f_X(x)}$

The third is really not okay.   Hints: $$\begin{align}\mathsf P(Y>t) ~=~& {\displaystyle\int_{t}^1} f_{Y}(y)\operatorname d y \\[2ex]~\mathsf P(Y>t\mid X=s) ~=~& {\displaystyle\int_{t}^1} f_{Y\mid X}(y\mid s)\operatorname d y\end{align}$$

Graham Kemp
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  • Hello! Thanks so much for responding. Do you by any chance know where I can find sample problems similar to this? I'm super lost as I don't even know where to start with the hint. – NookLines May 16 '16 at 22:35
  • @NookLines You calculated $f_Y(y)$ in part (a) by integrating $f(x,y)$ over the total domain for $X$. Now integrate $f_Y(y)$ over the partial domain $0.9\leq Y\leq 1$. $$\mathsf P(Y>0.9) ~=~\int_{0.9}^1 \tfrac 13(4y+1)\operatorname d y$$ Likewise in part (b) you would have found $f_{Y\mid X}(y\mid x)$ so use that to do the rest. – Graham Kemp May 16 '16 at 23:18