practice_problems/problems/unit-02/continuous-distribution/5

[giscus[bot]]

practice_problems/problems/unit-02/continuous-distribution/5

https://mids-w203.github.io/practice_problems/problems/unit-02/continuous-distribution/5.html

[awesome-eric]

(a) Take the derivative? If so, then it's 12x^2
(b) Sum up the probabilities from 0 to 1/2, or: 12(1/2)^2 - 0 = 3
(c) Same as (b), but from 1/3 to 2/3, or: 12(2/3)^2 - 12(1/3)^2 = 48
(d) Solve for 12x^2 = .5, or: x^2 = (.5/12), or: x = sqrt(.5/12)

[kubernatty]

(a) To find the distribution function of a density function, we need to integrate the density function