# A discrete random variable X has the following probability distributions (see table below). (iii) Find P(3 < x < 7)

 X 0 1 2 3 4 5 6 7 8 P(x) a 3a 5a 7a 9a 11a 13a 15a 17a

This is the third 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) $\sum p_i=1$
P(3 < x < 7)=$P(x=4)+P(x=5)+P(x=6)$
$\qquad\qquad=\large\frac{9}{81}+\frac{11}{81}+\frac{13}{81}=\frac{33}{81}$
$\qquad\qquad=\large\frac{11}{27}$