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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)

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 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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