2. Let $mathrm{X} $ be a continuous random variable with the cumulative distribution function $$ begin{array}...

 

Transcribed Image Text:

2. Let $\mathrm{X} $ be a continuous random variable with the cumulative distribution function $$ \begin{array} {11} \mathrm{F}(x)=0, & x <0, \\ \mathrm{F}(x)=\frac{3}{8} \cdot x, & 0 \leq x \leq 2, \\ \mathrm{-F}(x)=1-\frac{1}{x^{2}}, & x>2. \end{array} $$ a) Find the probability density function $f(x)$. b) Find the probability $\mathrm{P}(1 \leq \mathrm{X} \leq 4)$. c) Find $\mu_{X}=E(X) $. d) Find $\sigma_{X}=\operatorname(SD) (X) $. SS. SP.284 2. Let $\mathrm{X} $ be a continuous random variable with the cumulative distribution function $$ \begin{array} {11} \mathrm{F}(x)=0, & x <0, \\ \mathrm{F}(x)=\frac{3}{8} \cdot x, & 0 \leq x \leq 2, \\ \mathrm{-F}(x)=1-\frac{1}{x^{2}}, & x>2. \end{array} $$ a) Find the probability density function $f(x)$. b) Find the probability $\mathrm{P}(1 \leq \mathrm{X} \leq 4)$. c) Find $\mu_{X}=E(X) $. d) Find $\sigma_{X}=\operatorname(SD) (X) $. SS. SP.284