Question
Download Solution PDFk का मान जिसके लिए फलन
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {k{e^{ - 3x}},}&{x > 0}\\ 0&{elsewhere} \end{array}} \right.\)
प्रायिकता घनत्व फलन है, है
Answer (Detailed Solution Below)
3
Detailed Solution
Download Solution PDFदिया गया है
f(x) = { ke-3x, x > o
{ 0, elsewhere
प्रयुक्त संकल्पना
\( \smallint \limits_{ - \infty }^\infty f\left( x \right)dx \) = \( \smallint \limits_{ - \infty }^0 f\left( x \right)dx\) + \(\smallint \limits_0^\infty f\left( x \right)dx\) = 1
गणना
दिए गए भाग के अनुसार
⇒\( \smallint \limits_{ - \infty }^0 f\left( x \right)dx\) = 0
⇒ 0 + \(\smallint \limits_0^\infty f\left( x \right)dx\) = 0
⇒ ∫ke-3xdx = 1
⇒ k[-e-3x/3]
⇒ -k/3[e-∞- e0] = 1
⇒ -k/3(0 – 1) = 1
⇒ k./3 = 1
∴ PDF के लिए k का मान 3 है
Last updated on Jul 17, 2025
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