GATE (TF) Textile 2015 Question Paper Solution | GATE/2015/TF/12

Question 12 (Textile Engineering & Fibre Science)

If a continuous random variable $X$ has probability density function $f(x) = \begin{cases} ax^2, & 0\leq x\leq 1 \\ 0,& otherwise \end{cases}$ then the value of a is ___3___.

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$f(x) = \begin{cases} ax^2, & 0\leq x\leq 1 \\ 0,& otherwise \end{cases}$
PDF=1
$\int f(x) dx=1$
$\int_{0}^{1} (ax^2)=1$
$a[\frac{x^3}{3}]_{0}^{1}=1$
$a[\frac{1^3}{3}-0]=1$
$a\times \frac{1^3}{3}=1$
a=3 (Ans)

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