$$$n = 10$$$ ve $$$p = 0.175$$$ parametreli binom dağılımı için $$$P{\left(X = 1 \right)}$$$ değerini bulun

Binom dağılımının çeşitli değerlerini $$$n = 10$$$, $$$p = 0.175 = \frac{7}{40}$$$ ve $$$x = 1$$$ kullanarak hesaplayın.

Ortalama: $$$\mu = n p = \left(10\right)\cdot \left(\frac{7}{40}\right) = \frac{7}{4} = 1.75$$$A.

Varyans: $$$\sigma^{2} = n p \left(1 - p\right) = \left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right) = \frac{231}{160} = 1.44375$$$A.

Standart sapma: $$$\sigma = \sqrt{n p \left(1 - p\right)} = \sqrt{\left(10\right)\cdot \left(\frac{7}{40}\right)\cdot \left(1 - \frac{7}{40}\right)} = \frac{\sqrt{2310}}{40}\approx 1.201561484069792.$$$A

$$$P{\left(X = 1 \right)}\approx 0.309830084623023$$$A

$$$P{\left(X \lt 1 \right)}\approx 0.146062754179425$$$A

$$$P{\left(X \leq 1 \right)}\approx 0.455892838802448$$$A

$$$P{\left(X \gt 1 \right)}\approx 0.544107161197552$$$A

$$$P{\left(X \geq 1 \right)}\approx 0.853937245820575$$$A