Question
Download Solution PDFएक यादृच्छिक चर X का प्रायिकता घनत्व फलन f(x) = \(\frac{\pi}{10} sin \frac{\pi x}{5}\); 0 ≤ x ≤ 5 है। X का पहला चतुर्थक है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
∫f(x)dx
∫π/10 (sinπx/5) dx
let \(\frac{π x}{5}=t\)
For x = 0, t = 0
For x = 5, t = π
\(\frac{π dx}{5}=dt\)
\(\frac{π dx}{5}=dt\)
\(dx=\frac{5dt}{π}\)
The limits of the above integration will be from 0 to π
\(\frac{-1}{2}(cost)|_0^\pi\)
\(-\frac{1}{2}(cos\pi - cos0)\)
= 1
Last updated on Jul 8, 2025
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