Let X be a discrete valued random variable with cumulative dist. F(x) is/are correct:

The correct options are:
1. has jump discontinuity
2. is non decreasing F(x)

Let us analyze the properties of the cumulative distribution function (CDF), $F\left(x\right)$, for a discrete valued random variable $X$ step-by-step:

1. Non-decreasing Property:
By definition, the cumulative distribution function of a random variable $X$ is given by:
$F\left(x\right)=P(X\le x)$
If we choose two real numbers $x_1$ and $x_2$ such that $x_1<x_2$, the event $\{X\le x_1\}$ is contained within the event $\{X\le x_2\}$. Consequently, the probability must satisfy:
$F\left(x_1\right)\le F\left(x_2\right)$
This demonstrates that $F\left(x\right)$ is always a non-decreasing function. Therefore, the option is non decreasing F(x) is correct.

2. Jump Discontinuities:
For a discrete valued random variable $X$, the probability is concentrated at specific, isolated values (say, $x_i$ where $P(X=x_i)>0$). The CDF of a discrete random variable is a step function that remains constant in the intervals between these values and jumps abruptly at each point $x_i$. The size of the jump at any point $x=x_i$ is equal to the probability mass at that point:
$P(X=x_i)=F\left(x_i\right)-\underset{x\to x_i^{-}}{lim}F\left(x\right)$
Because of these step-like changes, the function contains jump discontinuities at all values of $x$ where the probability mass is non-zero. Therefore, the option has jump discontinuity is correct.

Why other options are incorrect:
- F(x) is left continuous: By mathematical convention, a cumulative distribution function is defined to be right-continuous, not left-continuous.
- always a positive F(x): The values of $F\left(x\right)$ are bounded such that $0\le F\left(x\right)\le 1$. For values of $x$ less than the smallest possible value that the random variable can take, $F\left(x\right)=0$. Thus, it is not always strictly positive.