Compute the Variance and Standard Deviation of a Discrete Random $x$

question 57

Multiple Choice

Compute the Variance and Standard Deviation of a Discrete Random Variable
-The random variable $x$ represents the number of tests that a patient entering a clinic will have along with the corresponding probabilities. Find the mean and standard deviation for the random variable $x$ .
$\begin{array}{l|c}\mathrm{x} & \mathrm{P}(\mathrm{x}) \\\hline 0 & \frac{3}{17} \\1 & \frac{5}{17} \\2 & \frac{6}{17} \\3 & \frac{2}{17} \\4 & \frac{1}{17}\end{array}$

• A) mean: 1.59; standard deviation: \(1.09\)
• B) mean: \(1.59\); standard deviation: \(3.72\)
• C) mean: \(2.52\); standard deviation: \(1.93\)
• D) mean: \(3.72\); standard deviation: \(2.52\)

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Definitions:

Edgeworth Box

A diagram used in economics to show the distribution of resources and the potential for gains from trade between two individuals or entities.

Efficient Allocation

An optimal distribution of resources where it is impossible to make someone better off without making someone else worse off.

Goods

Tangible products or commodities that can be bought, sold, or traded to satisfy wants or needs.

Pareto Optimal

A state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.