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In R, simulate 1000 pairs from (X, Y) and produce a scatterplot of your sample. Which scatter plot below matches most closely to the one you have produced?

Now simulate 10° pairs from (X,Y) and use this new sample to estimate Pr(2X + 3Y > 3). \text { A random variable } \underline{X} \in \mathbb{R}^{2} \text { has the bivariate normal distribution } \left(\begin{array}{l}

X \\

Y

\end{array}\right) \sim N_{2}\left[\left(\begin{array}{l}

1 \\

7

\end{array}\right),\left(\begin{array}{ll}

1 & 1 \\

1 & 4

\end{array}\right)\right] The random variable Z is defined by Z = 5X – 3Y. Which histogram below best represents the distribution of Z?

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