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How to graph probability density function when given density function

You can plot this function in Mathematica using:

Plot[Piecewise[{{0.075 x + 2, 3 <= x && x <= 5}},
0], {x, 0, 5}]

plot of fun

And then verify area using definite integral (from 0 to infinity):

Integrate[Piecewise[{{0.075 x + 0.2, 3 <= x && x
<= 5}}, 0], {x, 0, Infinity}]

(which results in 1).

You can of course calculate it by hand.

Integral represents area under the curve. When x is not in range [3,5] then area is always zero.

So your problem can be reduced to calculating integral from 0.075 x + 0.2, between 3 and 5.

Integral from (0.075 x + 0.2)dx equals to 0.2 x + 0.0375 x^2 + C. When calculated in range, equals to 1.9375 - 0.9375 = 1.





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