Question
Download Solution PDFयदि एक सतत यादृच्छिक चर x का प्रायिकता घनत्व फलन
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {3x^2,}&o\le x\le1\\ {0,}&{elsewhere} \end{array}} \right.\)
है, तो a का मान इस प्रकार क्या होगा कि P[x ≤ a] = P[x > a] है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {3x^2,}&o\le x\le1\\ {0,}&{elsewhere} \end{array}} \right.\)
गणना
P(X < a) = 1/a2 = \(\mathop \smallint \nolimits_0^a f\left( x \right)dx = 1/2\)
⇒ \(3\mathop \smallint \nolimits_0^a\)x2dx = 1/2
⇒ 3[x3/3]a0 = 1/2
⇒ 3 × (a3/3 - 0) = 1/2
⇒ a3 = 1/2
∴ a का मान इस प्रकार कि P[x ≤ a] = P[x > a], (1/2)1/3 है।
Last updated on Jul 12, 2025
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