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RANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsRANDOM VARIABLE ANE DISCRETE PROBABILITY DISTRIBUTION3 Marks
Question
Examine whether the following distribution is a probability distribution of a discrete random variable $X$ :$P(x)=\frac{x+2}{25} ; x=1,2,3,4,5$
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Answer

Here, $\mathrm{p}(\mathrm{x})=\frac{x+2}{25}$
Putting, $x=1,2,3,4,5$
$P(1)=\frac{1+2}{25}=\frac{3}{25}$
$ P(2)=\frac{2+2}{25}=\frac{4}{25}$
$ P(3)=\frac{3+2}{25}=\frac{5}{25}$
$ P(4)=\frac{4+2}{25}=\frac{6}{25}$
$ P(5)=\frac{5+2}{25}=\frac{7}{25}$
Now, by the definition of discrete probability distribution, we must have
$(1)\ p(x)>0$ and $(2)\ \sum p(x)=1$.
Now, $p\left(x_i\right)>0$ for $(i=1,2,3,4,5)$ and
$\sum p\left(x_i\right)=p(1)+p(2)+p(3)+p(4)+p(5)$
$ =\frac{3}{25}+\frac{4}{25}+\frac{5}{25}+\frac{6}{25}+\frac{7}{25}=1$
Thus, conditions of probability distribution of discrete random variable are satisfied.
So the given distribution is a probability distribution of a discrete random variable $X$.

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