A random variable $\mathrm{X}$ takes the values 0,1 and 2. If $P(X=1)=P(X=2)$ and $P(X=0)=0.4$, then the mean of the random variable $\mathrm{X}$ is

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Aicharya · Accepted Answer

We have, $P(X=1)=P(X=2)$ $ \frac{\lambda^1}{1 !} e^\lambda=\frac{\lambda^2}{2 !} e^\lambda \Rightarrow \lambda=2 $ Also, $P(X=0)+P(X=1)+P(X=2)=1$ $ \begin{aligned} & \Rightarrow \quad 0.4+P(X=1)+P(X=2)=1 \ & \Rightarrow \quad P(X=1)+P(X=2)=0.6=\frac{6}{10}=\frac{3}{5} \end{aligned} $ Also, $P(X=1)+P(X=1)=\frac{3}{5}$ [from (i)] $\begin{aligned} & \Rightarrow \quad P(X=1)=\frac{3}{10} \ & \Rightarrow \quad P(X=1)=P(X=2)=\frac{3}{10} \ & 	ext { Mean } X_0 P(X=0)+X_1 P(X=1)+X_2 P(X=2) \ & =0+1 \cdot \frac{3}{10}+2 \frac{3}{10}=\frac{9}{10}=0.9\end{aligned}$

A random variable $\mathrm{X}$ takes the values 0,1 and 2. If $P(X=1)=P(X=2)$ and $P(X=0)=0.4$, then the…

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