Find mX for the following discrete probability distribution

Find m_X for the following discrete probability distribution:

X

4

3

2

p

1/3

1/12

7/12

a. 1/3

b. .92

c. 3

d. 2.75

e. mx is undefined because this is not a valid probability distribution.

Solution

the random variable X takes the values 4,3,2 with corresponding probabilities 1/3,1/12,7/12 respectively

hence mX which means the mean of X is defined by

E[X]=sum(value of X*corresponding probabilities)

      =4*1/3+3*1/12+2*7/12

      =4/3+3/12+14/12=33/12=11/4=2.75

hence the correct option is option d) 2.75 [answer]