A random variable $X$ has probability distribution given by $\mathrm{P}\left( X=x \right)=\left\{ \b

Question

A random variable $X$ has probability distribution given by $\mathrm{P}\left( X=x ight)=\left\{ \begin{matrix} kx\left( 6-x ight),x=1,\ 2,\ 3,\ 4,\ 5 \ 0,\,\,\,\,\,\,\,\,\,\,\mathrm{otherwise} \\end{matrix} ight.$ Show that $k=\frac{1}{35}$ [1] Find the mean and variance of $X$. [3] $40$ independent observations of $X$ are taken. Find the probability that the sum of the $40$ observations of $X$ exceeds $110$. [3]

Accepted Answer

(ii) $\mathrm{E}(X) = 3$, $\mathrm{Var}(X) = 1.6$; (iii) $0.894$

RI Sampling Tutorial Q8

RI Sampling Tutorial Q8

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