Mathematics, 28.07.2019 03:00 Turtlelover05
For 0 ≤ x ≤ 1 let f(x) = kx(1 − x), where k is a constant. find the value of k such that f is a density function. 2. find the mean and variance of the distribution in the preceding exercise. gle. com/search? q=.+find+the+mean+and+variance+of+t he+distribution+in+the+preceding+ex ercise.& oq=.+find+the+mean+and+variance+of+ the+distribution+in+the+preceding+e xercise.& aqs=chrome..69i57.485j0j7& sourceid=chrome& ie=utf-8
Answers: 1
to be a proper density function, we need
![\mathbb E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=6\int_0^1x^2(1-x)\,\mathrm dx=\frac12](/tpl/images/0141/1052/41b78.png)
![\mathbb V[X]=\mathbb E[X^2]-\mathbb E[X]^2](/tpl/images/0141/1052/f2f46.png)
![\mathbb E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=6\int_0^1x^3(1-x)\,\mathrm dx=\frac3{10}](/tpl/images/0141/1052/646ef.png)
![\mathbb V[X]=\dfrac3{10}-\dfrac1{2^2}=\dfrac1{20}](/tpl/images/0141/1052/a1330.png)
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For 0 ≤ x ≤ 1 let f(x) = kx(1 − x), where k is a constant. find the value of k such that f is a dens...
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