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The random variable X has a probability distribution P (X) of the following form, where k is some number: (i) Determine the value of k.

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&i x=0\\ 2k, if& x=1\\ 3k, if& x=2\\ 0,& otherwise \end{matrix}\right.

            (a) Determine the value of k.

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Sum of probabilities of probability distribution of random variable is 1.

 

\therefore \, \, \, \, k+2k+3k+0=1

                                 6k=1

                                    k=\frac{1}{6}

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