Question answer all.. 5) Suppose the cumulative distribution function of the random variable X is 0 x < -2, F(x) = 0.25x + 0.5 - 2 < x < 2, 1 2 < x. Determine the probability density function. Then Find p(X > -1.5),p(X < 1.8) and p(-1 < X < 1)

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Transcribed Image Text: 5) Suppose the cumulative distribution function of the random variable X is 0 x < -2, F(x) = 0.25x + 0.5 - 2 < x < 2, 1 2 < x. Determine the probability density function. Then Find p(X > -1.5),p(X < 1.8) and p(-1 < X < 1)

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(5) probability density function f(x)=\frac{d}{d x}(f(x))P\left(x_{1} \leqslant x \leqslant x_{2}\right)=F\left(x_{2}\right)-F\left(x_{1}\right) \quad F(x)=P(x \leqslant x)\begin{aligned}P(x>-1.5) & =1-P(x<-1.5) \\& =1-F(-1.5) \\& =1-\left[\frac{1}{8}\right] \\& =\frac{7}{8}\end{aligned}CS Scanned with CamScanner\begin{aligned}P(x \leqslant 1.8) & =F(1.8) \\& =0.25(1.8)+0.5 \\& =0.45+0.5 \\& =0.95\end{aligned}\begin{aligned}P(-1 \leqslant x \leqslant 1) & =F(1)-F(-1) \\& =0.75-0.25 \\& =0.5\end{aligned}\begin{aligned}f(x) & =0.25 x+0.5 \\f(1) & =0.25+0.5 \\& =0.75 \\f(-1) & =-0.25+0.5 \\& =0.25\end{aligned}CS Scanned with CamScannerHope the answer is clear. If you satisfied with my answer then please upvote because it is very useful for experts.  ...