A tetrahedral die with its faces numbered $1$, $2$, $3$ and $4$ is thrown and the number of

Question

A tetrahedral die with its faces numbered $1$, $2$, $3$ and $4$ is thrown and the number of the face on which it lands is noted. The 'score' is double the number on which it lands. Find the expectation and variance of the 'score'. A new experiment is set up where the 'score' is the sum of the numbers obtained when the die is thrown twice. Find the expectation and the variance of this new 'score'.

Accepted Answer

Under the fair, independent-throw model: (a) expectation $5$, variance $5$. (b) expectation $5$, variance $\dfrac52$.

Probability distribution function of a derived variable

Probability distribution function of a derived variable

Solution:

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