TS EAMCET · Maths · Probability
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
- D 0.4
Answer & Solution
Correct Answer
(D) 0.4
Step-by-step Solution
Detailed explanation
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,…
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