Place eight chips in a bowl three of which have the number o

Place eight chips in a bowl: three of which have the number one,two of which have the number two, and three of which have thenumber three. Say each chip has the probability of 1/8 of beingdrawn at random. Let the random variable X equal the number on thechip that is selected so that the space of X is S={1,2,3}. Makereasonable probability assignments to each of these three outcomes and compute the mean ? and the variance ?2 of this probability distribution.

Solution

3 ---- 1s

2 ---- 2s

3 ---- 3s

Probability of getting 1 = 3/8

Probability of getting 2 = 2/8

Probability of getting 3 = 3/8

Mean = sigma xP = 1*3/8 + 2*2/8 + 3*3/8 = (3+4+9)/8 = 2

Variance = ?x²p ? ?²

= (1*3/8 + 4*2/8 + 9*3/8 ) - 4= 3/8 + 8/8 + 27/8 -4 = 38/8 - 4 = 0.75