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Q. 9 The random variable $X$ has a probability distribution $P(X)$ of the following form, where k is some number :

$P(X)=\left\{\begin{matrix} k,& if & x=0\\ 2k,& if& x=1\\ 3k,& if& x=2\\ 0,& otherwise& \end{matrix}\right.$

(b) Find $P\left ( X< 2 \right ),P\left ( X\leq 2 \right ),P\left ( X\geq 2 \right ).$

Answers (1)

best_answer

$P(X< 2)=P(X=0)+P(X=1)$

$=k+2k$

$=3k$

$=3\times \frac{1}{6}$

$= \frac{1}{2}$

$P(X\leq 2)=P(X=0)+P(X=1)+p(X=2)$

$=k+2k+3k$

$=6k$

$=6\times \frac{1}{6}$

$=1$

$P(X\geq 2)=P(X=2)+P(X> 2)$

$=3k+0$

$=3\times \frac{1}{6}=\frac{1}{2}$

Posted by

seema garhwal

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