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# A discrete random variable X has the following probability distributions (see table below). (i) Find the value of a

This is the first part of multipart q4

Toolbox:
• If $S$ is a sample space with a probability measure and $X$ is a real valued function defined over the elements of $S$, then $X$ is called a random variable.
• Types of Random variables :
• (1) Discrete Random variable (2) Continuous Random variable
• Discrete Random Variable :If a random variable takes only a finite or a countable number of values, it is called a discrete random variable.
• Continuous Random Variable :A Random Variable X is said to be continuous if it can take all possible values between certain given limits. i.e., X is said to be continuous if its values cannot be put in 1 − 1 correspondence with N, the set of Natural numbers.
• The probability mass function (a discrete probability function) p(x) is a function that satisfies the following properties :
• (1) $P(X=x)=p(x)=p_x$
• (2) $P(x)\geq 0$ for all real $x$
• (3) $\sum p_i=1$
$\sum p(x_i)=1$
$\therefore a+3a+5a+7a+9a+11a+13a+15a+17a=1$
$81a=1$
$a=\large\frac{1}{81}$