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Question

A random variable X takes the values 0, 1, 2, 3 and its mean is1.3. If P(X=3)=2P(X=1) and P(X=2)=0.3 , then P(X=0)=

A
0.1
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B
0.2
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C
0.3
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D
0.4
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Solution

The correct option is D 0.4
E[X]=3i=0xipi=0P(X=0)+1P(X=1)+2P(X=2)+3P(X=3)=1.31P(X=1)+20.3+32P(X=1)=1.3P(X=1)=0.1Nowusing3i=0pi=1=P(X=0)+P(X=1)+P(X=2)+P(X=3)P(X=0)+0.1+0.3+0.2=1P(X=0)=0.4

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