Statistics for Data Science II, Week-wise practice

Undated, Set week-01

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Question 1

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The joint pmf of two random variables $X$ and $Y$ is given by

$\begin{array}{c|ccc} X\\backslash Y & 0 & 1 & 2 \\ \hline 0 & 0.3 & 0.05 & 0.05 \\ 1 & 0.25 & 0.05 & 0.3 \end{array}$

Find $P(X=0,Y=0)$.

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The joint pmf of two random variables $X$ and $Y$ is given by $$\begin{array}{c|ccc} X\\backslash Y & 0 & 1 & 2 \\ \hline 0 & 0.3 & 0.05 & 0.05 \\ 1 & 0.25 & 0.05 & 0.3 \end{array}$$ Find $P(X=0,Y=0)$. The joint pmf of two random variables $X$ and $Y$ is given by $$\begin{array}{c|ccc} X\\backslash Y & 0 & 1 & 2 \\ \hline 0 & 0.3 & 0.05 & 0.05 \\ 1 & 0.25 & 0.05 & 0.3 \end{array}$$ Find the marginal probability $P(X=0)$. The joint pmf of two random variables $X$ and $Y$ is given by $$\begin{array}{c|ccc} X\\backslash Y & 0 & 1 & 2 \\ \hline 0 & 0.3 & 0.05 & 0.05 \\ 1 & 0.25 & 0.05 & 0.3 \end{array}$$ Find the marginal probability $P(Y=0)$.