$X$ denotes the random variable representing the number of thunderstorms occurring per month. The

Question

$X$ denotes the random variable representing the number of thunderstorms occurring per month. The probability distribution function of $X$ is given in the following table. $x$$0$$1$$2$$3$$4$ $\mathrm{P}(X=x)$$a$$0.2$$0.5$$0.1$$b$ State the values of $a$ and $b$ which maximizes the value of $\mathrm{E}\left( X \right)$.[2] Using these values of $a$ and $b$, Show that $\mathrm{Var}\left( X \right)=1.01$.[3] Two independent observations ${{X}_{1}}$ and are taken of $X$. Find $\mathrm{P}\left( {{X}_{1}}-{{X}_{2}}\ge 1 \right)$. Hence, or otherwise, find $\mathrm{P}\left( \left| {{X}_{1}}-{{X}_{2}} \right|\ge 1 \right)$.[5]

Accepted Answer

(i) ${a=0}$, ${b=0.2}$ (iii) ${0.33}$, ${0.66}$

2005 RJC P2 Q25 [Modified]

2005 RJC P2 Q25 [Modified]

Video Solution:

Solution:

Solution locked