Question

Suppose you are at the pet store shopping for a new kitten, but instead of choosing one yourself, the pet store chooses one randomly for you. There is a 0.1 probability that the kitten chosen is 10 centimeters long, a 0.3 probability that the kitten chosen is 20 centimeters long, a 0.1 probability that the kitten chosen is 30 centimeters long, and a 0.5 probability that the kitten chosen is 40 centimeters long. Let ​X​ be the random variable representing the length of the kitten chosen. Find ​Var(X)​.

Answer 1

X	P(X)	X*P(X)	X² * P(X)
10	0.1	1	10.0000
20	0.3	6	120.0000
30	0.1	3	90.0000
40	0.5	20	800

	P(X)	X*P(X)	X² * P(X)
total sum =	1	30	1020.00

mean = E[X] = Σx*P(X) =            30 cm

          
E [ X² ] = ΣX² * P(X) =            1020.00
          
variance = E[ X² ] - (E[ X ])² =            120.00

so, Var(X) = 120 cm²