RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION — Statistics STD 12 Commerce — Question
Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsRANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION1 Mark
Question
Define discrete probability distribution.
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Answer
Suppose, probability of a discrete random variable $X$ is $p\left[X=x_i\right]=p\left(x_i\right)$. If for $i=1,2,3$, $n ; p\left(x_i\right)>0$ and $\sum_{i=1}^n p\left(x_i\right)=1$,
then set of real values $\left\{p\left(x_1\right), p\left(x_2\right), \ldots \ldots ., p\left(x_n\right)\right\}$ is called probability distribution of a discrete random variable $X$. In tabular form it is written as under:
$\begin{array}{c|c|c|c|c|c|c|c}
\mathrm{X}=x_i & x_1 & x_2 & x_3 & \cdots \cdots \cdots \cdot & x_{n-1} & x_n & \text { Total} \\
\hline p\left(x_i\right) & p\left(x_1\right) & p\left(x_2\right) & p\left(x_3\right) & \cdots \cdots \cdots \cdot & p\left(x_{n-1}\right) & p\left(x_n\right) & \sum_i^n p\left(x_i\right)=1
\end{array}$
Here, $0 < p (x_i) < 1$ and $i = 1, 2, 3, …, n$
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