Question

Box contains 5 balls. Two are numbered 3, one is numbered 4, and two are numbered 5. The balls are mixed, and one is selected at random. After a ball is selected, it’s number is recorded. Then it is replaced. If the experiment is repeated many times, find the variance and standard deviation of the numbers of the balls.

Answer 1

number on ball,X	P(X)	X*P(X)	X² * P(X)
3	2/5=0.4	1.2	3.6
4	1/5=0.2	0.8	3.2
5	2/5=0.4	2	10

	P(X)	X*P(X)	X² * P(X)
total sum =	1	4	16.8

mean = E[X] = Σx*P(X) =            4
          
E [ X² ] = ΣX² * P(X) =            16.8
          
variance = E[ X² ] - (E[ X ])² =            0.8
          
std dev = √(variance) =            0.894427191