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The probability mass function of a random variable $X$ is $P(X=x)=\frac{5}{2^{5}} \quad$ if $\quad x=0,1,2,3,4,5$
$=0$
otherwise then, $P(X \leq 2)=$
Options:
$=0$
otherwise then, $P(X \leq 2)=$
Solution:
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Verified Answer
The correct answer is:
$P(X \geq 3)$
$\begin{aligned} \mathrm{P}(\mathrm{x} \leq 2) \quad &=\mathrm{P}(\mathrm{x}=0)+\mathrm{P}(\mathrm{x}=1)+\mathrm{P}(\mathrm{x}=2) \\ &=\frac{{ }^{5} \mathrm{C}_{0}}{2^{5}}+\frac{{ }^{5} \mathrm{C}_{1}}{2^{5}}+\frac{{ }^{5} \mathrm{C}_{2}}{2^{5}} \\ &=\frac{1}{2^{5}}(1+5+10)=\frac{16}{32} \\ \mathrm{P}(\mathrm{x} \geq 3) \quad &=\mathrm{P}(\mathrm{x}=3)+\mathrm{P}(\mathrm{x}=4)+\mathrm{P}(\mathrm{x}=5) \\ &=\frac{{ }^{5} \mathrm{C}_{3}}{2^{5}}+\frac{{ }^{5} \mathrm{C}_{4}}{2^{5}}+\frac{{ }^{5} \mathrm{C}_{5}}{2^{5}} \\ &=\frac{1}{2^{5}}(10+5+1)=\frac{16}{32} \end{aligned}$
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