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AP EAMCET2003MathematicsProbability

A random variate X takes the values 0,1,2,3 and its mean is 1.3. If P(X=3)=2 P(X=1) and P(X=2)=0.3 , then P(X=0) is equal to :

Options

  1. A0.1
  2. B0.2
  3. C0.3
  4. D0.4

Correct answer

D. 0.4

Step-by-step solution

Given that, Mean = X_k P(X=k)=1.3X₀ P(X=0)+X₁ P(X=1)+X₂ P(X=2)+X₃ P(X=3)=1.3 0 P(X=0)+1 P(X=1)+2 P(X=2)+3 P(X=3)=1.3 P(X=1)+2(0.3)+3.2 P(X=1)=1.3 7 P(X=1)=0.7 P(X=1)=0.1 Now, P(X=3) 2 P(X=1)=2(0.1)=0.2 Also, P(X=0)+P(X=1)+P(X=2)+P(X=3)=1 P(X=0)+0.2+0.3+0.2=1 P(X=0)=1-0.6=0.4

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