Statistics for Data Science II, Week-wise practice

Undated, Set week-02

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Question 1

+3−0Single correctInstructions

The joint pmf of $X$ and $Y$ is

$\begin{array}{c|cc} X\\backslash Y & 1 & 2 \\ \hline 0 & 0.3 & 0.2 \\ 1 & 0.3 & 0.2 \end{array}$

Are $X$ and $Y$ independent?

Select one option

• A.

  They are independent only if the table is symmetric

• B.

  Yes, $X$ and $Y$ are independent

• C.

  No, $X$ and $Y$ are not independent

• D.

  Independence cannot be decided from a joint pmf

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The joint pmf of $X$ and $Y$ is $$\begin{array}{c|cc} X\\backslash Y & 1 & 2 \\ \hline 0 & 0.3 & 0.2 \\ 1 & 0.3 & 0.2 \end{array}$$ Are $X$ and $Y$ independent? The joint pmf of $X$ and $Y$ is $$\begin{array}{c|ccc} X\\backslash Y & 1 & 2 & 3 \\ \hline 0 & 0.05 & 0.05 & 0.3 \\ 1 & 0.05 & 0.3 & 0.25 \end{array}$$ Are $X$ and $Y$ independent? The joint pmf of $X$ and $Y$ is $$\begin{array}{c|ccc} X\\backslash Y & 1 & 2 & 3 \\ \hline 0 & 0.1 & 0.04 & 0.06 \\ 1 & 0.3 & 0.12 & 0.18 \\ 2 & 0.1 & 0.04 & 0.06 \end{array}$$ Are $X$ and $Y$ independent?