Ano ang pagkakaiba ng X kung mayroon itong sumusunod na probabilidad na probabilidad: f (x) = {3x2 if -1 <x <1; 0 otherwise}

Sagot:

#Var = sigma ^ 2 = int (x-mu) ^ 2f (x) dx # na hindi maisulat bilang:

# sigma ^ 2 = intx ^ 2f (x) dx-2mu ^ 2 + mu ^ 2 = intx ^ 2f (x) dx - mu ^ 2 #

# sigma_0 ^ 2 = 3int_-1 ^ 1 x ^ 4dx = 3/5 x ^ 5 _- 1 ^ 1 = 6/5 #

Paliwanag:

Ipinapalagay ko na ang tanong na sinadya upang sabihin

#f (x) = 3x ^ 2 "for" -1 <x <1; 0 "otherwise" #

Hanapin ang pagkakaiba?

#Var = sigma ^ 2 = int (x-mu) ^ 2f (x) dx #

Palawakin:

# sigma ^ 2 = intx ^ 2f (x) dx-2mucancel (intxf (x) dx) ^ mu + mu ^ 2cancel (intf (x) dx) ^ 1 #

# sigma ^ 2 = intx ^ 2f (x) dx-2mu ^ 2 + mu ^ 2 = intx ^ 2f (x) dx - mu ^ 2 #

kapalit

# sigma ^ 2 = 3int_-1 ^ 1 x ^ 2 * x ^ 2dx -mu ^ 2 = sigma_0 ^ 2 + mu ^ 2 #

Saan, # sigma_0 ^ 2 = 3int_-1 ^ 1 x ^ 4dx # at # mu = 3int_-1 ^ 1 x ^ 3dx #

Kaya't makalkula natin # sigma_0 ^ 2 "at" mu #

sa pamamagitan ng mahusay na proporsyon # mu = 0 # tingnan natin:

# mu = 3int_-1 ^ 1 x ^ 3dx = 3 / 4x ^ 4 _- 1 ^ 1 = 3/4 1-1 #

# sigma_0 ^ 2 = 3int_-1 ^ 1 x ^ 4dx = 3/5 x ^ 5 _- 1 ^ 1 = 6/5 #