Given Independent Random Variables with Means and Standard Deviations as Shown,find

question 195

Multiple Choice

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 0.3Y. $$\begin{array} { c | c c } & \text { Mean } & \text { SD } \\\hline \mathrm { X } & 70 & 7 \\\mathrm { Y } & 60 & 8\end{array}$$

• A)? = 18,? = 0.72
• B)? = 60.3,? = 8
• C)? = 60.3,? = 2.4
• D)? = 18,? = 8
• E)? = 18,? = 2.4

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Definitions:

Payoff Table

A decision-making tool that outlines the outcomes of different decisions under various states of nature, helping in analyzing potential payoffs.

Maximin Criterion

A decision rule used in statistics and game theory that focuses on maximizing the minimum payoff or outcome attainable, often applied under conditions of uncertainty.

Expected Value of Perfect Information (EVPI)

A concept in decision theory that represents the maximum amount a decision-maker would be willing to pay for having perfect information before making a decision, highlighting the value of removing all uncertainty.

Prune the Branch

A strategy in decision-making and optimization processes that involves eliminating options or paths that are unlikely to lead to the best outcome.