[Q3] The joint probability distribution is y fxx(x,y) 0 1/4 0 1/4 1/4 1/4 Show that the correlation between X and Y is zero, but X and Y are not independent.
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The table provided seems to be formatted incorrectly in the query. Let's assume the correct format is as follows, where the rows represent the values of X and the columns represent the values of Y: | X\Y | 0 | 1 | |-----|-----|-----| | 0 | 1/4 | 1/4 | | 1 Show moreā¦
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The joint probability distribution is $$ \begin{array}{lcccc} x & -1 & 0 & 0 & 1 \\ y & 0 & -1 & 1 & 0 \\ f_{X Y}(x, y) & 1 / 4 & 1 / 4 & 1 / 4 & 1 / 4 \end{array} $$ Show that the correlation between $X$ and $Y$ is zero but $X$ and $Y$ are not independent.
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The joint probability distribution is $$ \begin{array}{llcll} x & -1 & 0 & 0 & 1 \\ y & 0 & -1 & 1 & 0 \\ f_{X Y}(x, y) & 1 / 4 & 1 / 4 & 1 / 4 & 1 / 4 \end{array} $$ Show that the correlation between $X$ and $Y$ is zero, but $X$ and $Y$ are not independent.
Let $X$ and $Y$ have the joint distribution given in Problem 1 of Chapter 3 a. Find the covariance and correlation of $X$ and $Y$. b. Find $E(Y | X=x)$ for $x=1,2,3,4 .$ Find the probability mass function of the random variable $E(Y | X)$.
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