A discrete distribution is one in which the random variable can take only a limited number of values.
A cumulative distribution, which can be discrete of continuous, is the sum (if discrete) or integral (if continuous) of the probabilities of all events for which the random variable is less than or equal to the given value.
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A simple continuous distribution can take any value between two other values whereas a discrete distribution cannot.
A cumulative frequency polygon has straight lines connecting the points. A normal cumulative frequency diagram uses a smooth curve to join the points.
The difference between frequency polygon and line graphs is their purpose. Frequency polygons are for understanding shapes distributions, while line graphs shows information that is related in some way.
A convolution is a function defined on two functions f(.) and g(.). If the domains of these functions are continuous so that the convolution can be defined using an integral then the convolution is said to be continuous. If, on the other hand, the domaisn of the functions are discrete then the convolution would be defined as a sum and would be said to be discrete. For more information please see the wikipedia article about convolutions.
I think you are going for continuous variable, as compared with discrete variables.