The probability distribution of a discrete random variable $X$ is given by \(\mathrm{P}(X = x) = k

Question

The probability distribution of a discrete random variable $X$ is given by $\mathrm{P}(X = x) = k\left(\frac{2}{3}\right)^x$ where $x = 0, 1, 2, 3, \dots$ Show that $\mathrm{P}(X \leq x) = 3k\left[1 - \left(\frac{2}{3}\right)^{x+1}\right]$, where $x = 0, 1, 2, 3, \dots$ Hence or otherwise, find the value of $k$.

Accepted Answer

(b) $ \frac{1}{3}$.

Cumulative distribution function of a DRV

Cumulative distribution function of a DRV