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Question Bank [2022] — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Question Bank [2022]4 Marks
Question
The p.d.f. of a continuous r.v. $X$ is
$
f(x)=\left\{\begin{array}{ll}
\frac{3 x^2}{8} & 00 & \text { otherwise }
\end{array}\right.
$
Determine the c.d.f. of $X$ and hence find $P(X<-2)$
✓

Answer

$ F ( x )=\int_0^x f(x) \cdot d x$
$=\int_0^x \frac{3 x^2}{8} \cdot d x$
$=\frac{3}{8} \int_0^x x^2 \cdot d x$
$=\frac{1}{8}\left[x^3\right]_0^x$
$=\frac{x^3}{8}$
$P(X<-2)=F(-2)$
$F ( x )=0 \quad \ldots\left[ F (x)=0 \text { if } x \notin(0,2)$
$\therefore F (x)=1 \text { for } x \leq 0\right]$

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