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

Question

random variable $X$ has probability distribution given by $\mathrm{P}\left( X=x ight)=\left\{ \begin{matrix} kx\left( 6-x ight),\,\,\,x=1,2,3,4,5 \ 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{otherwise}\mathrm{.} \ \end{matrix} ight.$ 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] Find the probability that the maximum value observed is $5$. [3]

Accepted Answer

$k = \dfrac{1}{35}$; E(X) = 3, Var(X) = 1.6; 0.894; 0.998

2021 TJC P2 Q9

2021 TJC P2 Q9

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