MathProbabilityContinuous random variables

Continuous random variable

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Suppose now that Alice wants to describe her walk via continuous random variables. This approach is natural because the speed of walk (measured as km/h) varies in the appropriate range of values. She's got the following probability density function:

f(x)={0,x<0x8,0x40,x>4f(x)= \left\{\begin{matrix} 0, x< 0\\ \frac{x}{8},0\leq x\leq 4 \\ 0, x>4 \end{matrix}\right.

Calculate the probability of the event that Alice's speed during the walk does not exceed 3 km/h, but never drops below 1 km/h.

You need to put a real number accurate to one decimal place.

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