You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
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It is a discrete random variable.
continuous random variable
Zero.
A discrete random variable is a variable that can only take some selected values. The values that it can take may be infinite in number (eg the counting numbers), but unlike a continuous random variable, it cannot take any value in between valid results.
The random variable is discrete