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This question was given to me as a review for an upcoming exam.

Calculate the constant $c$:

$$f_X(x) =\begin{cases} c * \ln(x) & 1 \leq x \leq 2 \\ 0 & \text{otherwise} \end{cases} $$

My work:

$f_X(x) = 1$

$\int_1^2c*\ln(x) dx = 1$

$c *\int_1^2\ln(x) dx = 1$

$c * (2\ln(2) -1) = 1$

$c = \frac{1}{2\ln(2) -1}$

Did I do this correctly?

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  • 5
    $\begingroup$ It looks ok to me. $\endgroup$ – paw88789 Apr 1 at 18:20
  • 2
    $\begingroup$ Save that the start should clearly be $\int_\Bbb R f_X(x)~\mathrm d x=1$ $\endgroup$ – Graham Kemp Apr 1 at 22:17

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