A random variable $\mathrm{X}$ takes the values $0,1,2$. Its mean is $1 \cdot 2 .$ If…
A random variable $\mathrm{X}$ takes the values $0,1,2$. Its mean is $1 \cdot 2 .$ If $\mathrm{P}(\mathrm{X}=0)=0.3$,
then $\mathrm{P}(\mathrm{X}=1)=$
- $0.1$
- $0.5$
- $0.2$
- $0.4$
Solution
Random variable
$\begin{array}{l}
x \text { takes }=0,1,2 \\
\sum x_{i} P\left(x_{i}\right)=\text { Mean } \\
1.2=(0 * 0.3)+1 \times P(x=1)+2 \times P(x=2) \\
P(x=1)+2 P(x=2)=1.2 \rightarrow(1) \\
P(x=1)+P(x=2)+P(x=0)=1 \\
P(x=1)+P(x=2)=0.7 \rightarrow(2)
\end{array}$
By Solving (1) \& (2)
$\begin{array}{l}
P(x=2)=0.5 \\
P(x=1)=0.2 .
\end{array}$
Asked in: MHT CET 2020 (12 Oct Shift 1)
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