An unbiased die is in the form of a regular tetrahedron and has its faces numbered $1$, $2$, \(3

Question

An unbiased die is in the form of a regular tetrahedron and has its faces numbered $1$, $2$, $3$, $4$ and when the die is thrown onto a horizontal table, the number of the face in contact with the table is noted. Two such dice are thrown and the score $X$ is found by multiplying these numbers together. Obtain the probability distribution of $X$ Derive the values of $P(X > 8)$; $E(X)$; $Var(X)$.

Accepted Answer

(i) $P(X = k) = \frac{1}{16}, k=1,9,16; P(X = m) = \frac{1}{8}, m =2,3,6,8,12; P(X=4) = \frac{3}{16}$; (ii) (a) $\frac{1}{4} $ ; (b) $ \frac{25}{4} $ ; (c) $ \frac{275}{16} $.

Possibility table and probability distribution function of a derived variable

Possibility table and probability distribution function of a derived variable