Question

A unitörm distribution has a mean oft and Variance 4/3. Find P(Xe0).

Answer 1

$$\mu=\dfrac{A+B}{2}=1$$

$$\sigma^2=\dfrac{(B-A)^2}{12}=\dfrac{4}{3}$$

$$A+B=2$$

$$B-A=4$$

$$A=-1, B=3$$

$$f(x)= \begin{cases} \dfrac{1}{3-(-1)} &-1\leq x\leq 3 \\ 0 & otherwise \end{cases}$$

$$P(X<0)=\displaystyle\int_{-1}^{0}\dfrac{1}{4}dx=[\dfrac{1}{4}x]\begin{matrix} 0 \\ -1 \end{matrix}=\dfrac{1}{4}$$

$$P(X<0)=0.25$$