Question
Download Solution PDFThe value of k for which the function
\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {k{e^{ - 3x}},}&{x > 0}\\ 0&{elsewhere} \end{array}} \right.\)
is probability density function, is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
f(x) = { ke-3x, x > o
{ 0, elsewhere
Concept used
\(\smallint \limits_{ - \infty }^\infty f\left( x \right)dx \) = \( \smallint \limits_{ - \infty }^0 f\left( x \right)dx\) + \(\smallint \limits_0^\infty f\left( x \right)dx\) = 1
Calculation
According to given part
⇒\(\smallint \limits_{ - \infty }^0 f\left( x \right)dx\) = 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
∴ The value of k = 3 for PDF
Last updated on Jun 13, 2025
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