Question

The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the mean and standard deviation.

  x         P(x)

                                     1        0.14

                                     2           ?

                                     3        0.12

4 0.14

                                     5        0.13

                                     6        0.31

Answer 1

To calculate mean and standard deviation we first need to calculate the probability corresponding to 2

Sum of P(x) should be 1

Here, the sum is 0.84

P(x=2) = 1 - 0.84

P(x=2) = 0.16

X	P(X)	X*P(X)	X^2*P(X)
1	0.14	0.14	0.14
2	0.16	0.32	0.64
3	0.12	0.36	1.08
4	0.14	0.56	2.24
5	0.13	0.65	3.25
6	0.31	1.86	11.16
Total	1	3.89	18.51

Mean = sum(X*P(X))

Mean = 3.89

Variance = sum(X^2*P(X)) - sum(X*P(X))^2

Variance = 18.51 - 3.89^2

Variance = 18.51 - 15.1321

Variance = 3.3779

Standard deviation = sqrt(Variance)

Standard deviation = sqrt(3.3779)

Standard deviation = 1.8379