NIELIT 2018-14

Question

A continuous random variable $x$ is distributed over the interval $[0,2]$ with probability density function $f(x) =ax^2 +bx$, where $a$ and $b$ are constants. If the mean of the distribution is $\frac{1}{2}$. Find the values of the constants $a$ and $b$.

• A. $a=2, b=- \frac{13}{6}$
• B. $a= – \frac{15}{8}, b=3$
• C. $a= – \frac{29}{6}, b=2$
• D. $a=3, b= – \frac{7}{2}$

Comments

options A,B and D are satisfying the answer

please confirm

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$\int_{0}^{2}(ax^2 +bx)dx = 1$ gives $8a + 6b = 3$

$\int_{0}^{2}x(ax^2 +bx)dx = 1/2$ gives $24a + 16b = 3$

So, $a=\frac{-15}{8}, b= 3$

Answer 1

Answer is B