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

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- 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)=$P(x=4)+P(x=5)+P(x=6)$

$\qquad\qquad=\large\frac{9}{81}+\frac{11}{81}+\frac{13}{81}=\frac{33}{81}$

$\qquad\qquad=\large\frac{11}{27}$

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