Determine the probability density function for the following cumulative distribution function. F(x) = { 0 x < -2 0.25x + 0.5 -2 <= x < 1 0.5x + 0.25 1 <= x < 1.5 1 1.5 <= x } Find the value of the probability density function at x = -0.3.
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The CDF is given in a piecewise form: F(x) = \begin{cases} 1 & x < -2 \\ 0.25x + 0.5 & -2 \leq x < 2 \\ 0.5x + 0.25 & 2 \leq x < 5 \\ 1 & x \geq 5 \end{cases} To find the pdf, we need to take the derivative of the CDF with respect to x. We will do this for each Show more…
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