Q.The probability distribution function of a discrete random Variable $X$ is : $f(x)=\begin{cases}2k, & x=1\\3k, & x=3\\4k, & x=5\\0, & \text{otherwise}\end{cases}$ where $k$ is some constant, find $k$.

For a discrete random variable, the probability mass function (p.m.f.) $p(x_i)=P(X=x_i)$ gives the probability of each individual value, subject to $p_i\geq0$ and $\sum p_i=1$. For a continuous random variable, the probability density function (p.d.f.) $f(x)$ plays the analogous role, subject to $f(x)\geq0$ and $\int_{-\infty}^{\infty}f(x)\,dx=1$ …