Find the expected value of a random variable x having the
following probability distribution.
x
0
1
2
3
14
5
Probability
1/8
1/4
3/16
1/4
1/16
1/8

2.25

Step-by-step explanation:

Given the following:

x = - - - 0 - - 1 - - 2 - - 3 - - 4 - - 5

P(x) - 1/8, 1/4, 3/16, 1/4, 1/16, 1/8

Expected value = sum of [x * p(x)]

sum of [x * p(x)] = (0*1/8) + (1*1/4) + (2*3/16) + (3*1/4) + (4*1/16) + (5*1/8)

= 0 + 1/4 + 6/16 + 3/4 + 4/16 + 5/8

= 0 + 1/4 + 3/8 + 3/4 + 1/4 + 5/8

Take L. C. M

=0 + (2 + 3 + 6 + 2 + 5) / 8

= 0 + 18/8

= 0 + 2.25

= 2.25