JEE Mains · Maths · STD 12 - 13. probability
If the probability that the random variable \(X\) takes values \(x\) is given by \(P ( X = x )= k ( x +1) 3^{- x }, x =0\), \(1,2,3 \ldots\), where \(k\) is a constant, then \(P ( X \geq 2)\) is equal to
- A \(\frac{7}{27}\)
- B \(\frac{11}{18}\)
- C \(\frac{7}{18}\)
- D \(\frac{20}{27}\)
Answer & Solution
Correct Answer
(A) \(\frac{7}{27}\)
Step-by-step Solution
Detailed explanation
\(\sum \limits_{x=0}^{\infty} P ( X = x )=1\) \(k \left(1+2 \cdot 3^{-1}+3 \cdot 3^{-2}+4 \cdot 3^{-3}+\ldots \infty\right)=1\) \(\text { Let } \quad s =1+\frac{2}{3}+\frac{3}{3^2}+\frac{4}{3^3}+\ldots \infty\)…
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