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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 :

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

(a) Determine the value of $\inline k.$

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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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