Problem: A biased four-sided dice with faces numbered $1, 2, 3$ and $4$ is rolled. The number on the bottommost face is modelled as a random variable $X$. Given that
\[
P(X = x) = \frac{k}{x}.
\]
-
Find the value of $k$.
-
Give the probability distribution of $X$ in table form.
-
Find the probability that
\[
\text{(i) } X > 2, \quad \text{(ii) } 1 < X < 4 \quad \text{(iii) } X > 4.
\]
Solution: I encourage you to attempt to solve the problem today. The solution will be provided tomorrow. This will give you the opportunity to test your understanding of the problem and to improve your skills in solving similar problems in the future.