Question

For the following probability distribution, please compute the following: µ, σ, and the median.

y	3	5	6	8	10
Pr(y)	.15	.10	.30	.20	.25

Answer 1

Solution:

y	P(y)	y*P(y)	y2*P(y)
3	0.15	0.45	1.35
5	0.10	0.50	2.50
6	0.30	1.80	10.80
8	0.20	1.60	12.80
10	0.25	2.50	25.00

Mean:

Standard Deviation:

where

thus

(Round final answer to specified number of decimal places)

Median:

To find median find cumulative probability distribution (CDF) .

y	P(y)	CDF: P( Y ≤ y)
3	0.15	0.15
5	0.10	0.25
6	0.30	0.55
8	0.20	0.75
10	0.25	1.00

Median is the y value for which CDF is 0.50 or more at first time.

Thus from above CDF = 0.55 is more than 0.50 for first time.

Thus corresponding y value = 6

thus median = 6