Etsi $$$P{\left(X = 3 \right)}$$$ eksponenttijakaumalle, kun $$$\lambda = 0.5$$$

Laske eksponenttijakaumalle eri arvot käyttäen $$$\lambda = 0.5 = \frac{1}{2}$$$ ja $$$x = 3$$$.

Keskiarvo: $$$\mu = \frac{1}{\lambda} = 2$$$A.

Varianssi: $$$\sigma^{2} = \frac{1}{\lambda^{2}} = 4$$$A.

Keskihajonta: $$$\sigma = \sqrt{\frac{1}{\lambda^{2}}} = 2$$$A.

$$$P{\left(X = 3 \right)} = 0$$$A

$$$P{\left(X \lt 3 \right)}\approx 0.77686983985157$$$A

$$$P{\left(X \leq 3 \right)}\approx 0.77686983985157$$$A

$$$P{\left(X \gt 3 \right)}\approx 0.22313016014843$$$A

$$$P{\left(X \geq 3 \right)}\approx 0.22313016014843$$$A