MHT CET · Maths · Probability
If a random variable X has the p.d.f.
\(\mathrm{f}(x)=\left\{\begin{array}{cl}\frac{\mathrm{k}}{x^2+1} & , \text { if } 0 < x < \infty \\ 0 & , \text { otherwise }\end{array}\right.\)
then c.d.f. of X is
- A \(2 \tan ^{-1} x\)
- B \(\frac{\pi}{2} \tan ^{-1} x\)
- C \(\frac{2}{\pi} \tan ^{-1} x\)
- D \(\tan ^{-1} x\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{\pi} \tan ^{-1} x\)
Step-by-step Solution
Detailed explanation
\( \int_{0}^{\infty} \frac{\mathrm{k}}{x^2+1} \, dx = 1 \) \( \mathrm{k} [\tan^{-1} x]_{0}^{\infty} = 1 \)
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