Capitolo 8

1. $48.4\,\%$.

2. $f(x) = 2x$; $\mu=2/3$; $\sigma=0.24$.

3. E$[(X-\mu)/\sigma] = ($E$(X)-\mu)/\sigma = 0$.
   $Var[(X-\mu)/\sigma] =$   Var$(X)/\sigma^2$ = 1.
4. $F(x)$ non può essere decrescente!

5. $k=-1$; $1 \le x \le 4$;
   $f(x)=1/(2\, \sqrt{x})$;
   E$(X) = 7/3 = 2.33$; Var$(X) = 34/45 = 0.75$; $\sigma = 0.87$.
   Come mai $\sigma \approx 3/\sqrt{12}$ ?

6. 0.30854; 0.09185; 0.69146; 0.34134; 0.47725; 0.9973.

7. $5.74\cdot 10^{-7}$

8. $G(t)= 1/(1-\lambda\, t)$; E$(X)= \lambda$; $\sigma = \lambda$.

9. $\le 2.3 \,\%$

10. $20.6\,\%$.

11. $G(t)= 1/(1-\lambda\, t)$; E$(X)= \lambda$; $\sigma = \lambda$.