Q55 / 160 · TS EAMCET 2003 · Mathematics

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 :

  • A
    0.1
  • B
    0.2
  • C
    0.3
  • Correct answer
    D
    0.4

Solution

Given that, Mean $=\Sigma X_k P(X=k)=1.3$ $X_0 P(X=0)+X_1 P(X=1)+X_2 P(X=2)+X_3 P(X=3)=1.3$ $\Rightarrow 0 \cdot P(X=0)+1 \cdot P(X=1)+2 P(X=2)$ $+3 \cdot P(X=3)=1.3$ $\Rightarrow P(X=1)+2(0.3)+3.2 P(X=1)=1.3$ $\Rightarrow 7 P(X=1)=0.7 \Rightarrow P(X=1)=0.1$ Now, $P(X=3) 2 P(X=1)=2(0.1)=0.2$ Also, $P(X=0)+P(X=1)+P(X=2)+P(X=3)=1$ $\Rightarrow P(X=0)+0.2+0.3+0.2=1$ $\therefore P(X=0)=1-0.6=0.4$

Hence, the correct answer is option: 'D'.

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