engineering recuitment GATE ME 2023-24 Test Series Engineering Mathematics Probability and Statistics Random Variables Basics
A random variable X has a probability density function \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {k\;{x^n}{e^{ - x}}\;;\;x \ge 0}\\ {0\;;\;otherwise} \end{array}} \right.\) (n is an integer) with mean 3. The values of {k, n} are
1
\(\left\{ {\frac{1}{2},\;1} \right\}\)
2
\(\left\{ {\frac{1}{4},\;2} \right\}\)
3
\(\left\{ {\frac{1}{2},\;2} \right\}\)
4
{1, 2}