Obtain the Probability Distribution of the Random Variable A) B)

question 78

Multiple Choice

Obtain the probability distribution of the random variable.
-The following table displays a frequency distribution for the number of living grandparents for students at a high school. For a randomly selected student in the school, let X denote the number of Living grandparents of the student. Obtain the probability distribution of X. $\begin{array}{r|rrrrr}\text { Number of living grandparents } & 0 & 1 & 2 & 3 & 4 \\\hline \text { Frequency } & 38 & 85 & 157 & 216 & 154\end{array}$

• A)
• \(\begin{array}{r|r}
• \text { Grandparents } & \text { Probability } \\
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.066 \\
• 1 & 0.146 \\
• 2 & 0.242 \\
• 3 & 0.317 \\
• 4 & 0.229
• \end{array}\)
• B)
• \(\begin{array}{r|r}
• \text { Grandparents } & \text { Probability } \\
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.2 \\
• 1 & 0.2 \\
• 2 & 0.2 \\
• 3 & 0.2 \\
• 4 & 0.2
• \end{array}\)
• C)
• \(\begin{array}{r|r}
• \text { Grandparents } & \text { Probability } \\
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 1 & 0.139 \\
• 2 & 0.257 \\
• 3 & 0.353 \\
• 4 & 0.252
• \end{array}\)
• D)
• \(\begin{array}{r|r}
• \text { Grandparents } & \text { Probability } \\
• \mathrm{x} & \mathrm{P}(\mathrm{X}=\mathrm{x}) \\
• \hline 0 & 0.058 \\
• 1 & 0.131 \\
• 2 & 0.242 \\
• 3 & 0.332 \\
• 4 & 0.237
• \end{array}\)

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Definitions:

Option Contract

A contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a certain date.

Specific Asset

A distinct item of property owned by a person or company, regarded as having value and available to meet debts, commitments, or legacies.

Specific Price

This term refers to the exact price of a particular item or security at a specified time.

Put Option

A put option is a financial contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying asset at a set price within a specified time.