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Assertion: A random variable X takes the values 0,1,2. It’s mean is 0.6. If P(X = 0) = 0.5 then P(X =1) = 0.4
Reason : If X : S→R is a discrete random variable with range {x₁, x₂, x₃,....} then mean $= \sum_{r = 1}^{\infty} X_{r} P (X = X_{r})$

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Detailed Solution

X=x	0	1	2
P(X=x₁)	0.5	s	t

$0.5 + s + t = 1 \Rightarrow s + t = 0 .5$

$μ = s + 2 t = 0 .6 \Rightarrow t = 0 .1, s = 0 .4$

$\Rightarrow P (X = 1) = 0 .4$

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