(a) A Random variable has the following probability distribution $$ \begin{array}{ccccc} X & 0 & 1 & 2 & 3 \\ f(x) & \mathrm{k} / 2 & \mathrm{k} / 3 & \frac{k+1}{3} & \frac{2 k+1}{3} \end{array} $$ Find (i) $k$ (ii) Mean (iii) variance (iv) Distribution function. ..... 7
Explanation
The problem requires us to find the value of k, the mean, the variance, and the distribution function of a discrete random variable with a given probability distribution.
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