A man has $n$ similar keys, only one of which will open his safe. Let the random variable $X$ be the

Question

A man has $n$ similar keys, only one of which will open his safe. Let the random variable $X$ be the number of attempts he requires to open his safe. Find the probability distribution of $X$ in terms of $n$. Find $\mathrm{E}\left( X \right)$ and $\mathrm{Var}\left( X \right)$. (You may use the result $\sum\limits_{r=1}^{n}{{{r}^{2}}=\frac{n\left( n+1 \right)\left( 2n+1 \right)}{6}}$.)

Accepted Answer

$E(X) = \frac{1}{2}(1+n)$; $\text{Var}(X) = \frac{n^2-1}{12}$

ACJC Tutorial 26 Q11

ACJC Tutorial 26 Q11

Video Solution:

Solution:

Solution locked