Question

An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf
x =16, p(x) = .2
x= 18, p(x) = .5
x=20, p(x) = .3
Compute E(X), E(X2), and V(X).

Answer 1

Answer:

E(x)=18.2

E(x²)=333.2

V(x)=1.96

Step-by-step explanation:

Given that

x=16, p(x) =0 .2

x= 18, p(x) =0 .5

x=20, p(x) = 0.3

E(x)  :

$E(x)=\sum xp(x)\\E(x)=16\times 0.2+18\times 0.5+20\times 0.3\\E(x)=18.2$

E(x²) :

$E(x^2)=\sum x^2p(x)\\E(x^2)=16^2\times 0.2+18^2\times 0.5+20^2\times 0.3\\E(x^2)=333.2$

V(x) ::

$V(x)=E(x^2)-(E(x))^2\\V(x)=333.2-(18.2)^2\\V(x)=1.96$