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The Following Table Is a Valid Probability Distribution, for a Random

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The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. XP[X]32012\begin{array} { | c | c | } \hline X & P [ X ] \\\hline - 3 & \\\hline - 2 & \\\hline 0 & \\\hline 1 & \\\hline 2 & \\\hline\end{array} Which of the following statements is correct ? AThe expected value of X can only be 0 . B The expected value of X could be 3 .C The expected value of X could be 0.5DNone of these choices are correct \begin{array}{|l|l|}\hline A&\text {The expected value of \( \mathrm{X} \) can only be 0 . }\\\hline B&\text { The expected value of \( \mathrm{X} \) could be 3 .}\\\hline C&\text { The expected value of \( \mathrm{X} \) could be 0.5}\\\hline D&\text {None of these choices are correct }\\\hline \end{array}

Understand the concept of Arrow's impossibility theorem and its implications for social choice theory.
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Explain the concept of asymmetric information and how it leads to problems like moral hazard and adverse selection.

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