Find the Specified Probability Distribution of the Binomial Random Variable $\begin{array}{r|r}\mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\\hline 0 & 0.4219 \\1 & 0.4219 \\2 & 0.1286 \\3 & 0.0276\end{array}$

question 129

Multiple Choice

Find the specified probability distribution of the binomial random variable.
-In one city, 25% of the population is under 25 years of age. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that are under 25
Years of age.

• A)
• \(\begin{array}{r|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.4219 \\
• 1 & 0.4219 \\
• 2 & 0.1286 \\
• 3 & 0.0276
• \end{array}\)
• B)
• \(\begin{array}{c|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.4219 \\
• 1 & 0.4219 \\
• 2 & 0.1406 \\
• 3 & 0.0156
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.4219 \\
• 1 & 0.1406 \\
• 2 & 0.0469 \\
• 3 & 0.0156
• \end{array}\)
• D)
• \(\begin{array}{r|r}
• \mathrm{X} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 1 & 0.25 \\
• 2 & 0.0625 \\
• 3 & 0.0156
• \end{array}\)

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Definitions:

Socially Optimal Price

This is the price point at which the social benefits of product consumption match the overall cost of production, aiming for an efficient allocation of resources.

Natural Monopoly

A type of monopoly that exists due to the high fixed or startup costs of operating a business in a specific industry, making it inefficient for more than one firm to operate.

Marginal Cost

The increase in cost resulting from the production of one additional unit of a product.

Demand Curve

A graphical illustration that demonstrates the link between the cost of an item and how much of it consumers are willing to buy.