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Q)

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

 

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

This is the second part of multipart q4 

 

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A)
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) $\sum p_i=1$
$P(x<3)=P(x=0)+P(x=1)+P(x=2)$
$\qquad\quad\;\;=\large\frac{1}{81}+\frac{3}{81}+\frac{5}{81}$
$\qquad\quad\;\;=\large\frac{9}{81}$
$\qquad\quad\;\;=\large\frac{1}{9}$
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