Question

Find the standard deviations of the random variables. a) X P(X = x) X P(X = x) 10 | 0.2 1 | 0.4 20 0.5 3 0.2 30 0.3 5 0.1 b) 7 0.3

Can you help me with A & B

​a) To find the standard deviation

b) find the standard deviation

Answer 1

a)

Mean = $\sum$ X * P(X)

= 10 * 0.2 * 20 * 0.5 + 30 * 0.3

= 21

Standard deviation = sqrt [ $\sum$ X² * P(X) - Mean² ]

= sqrt [ 10² * 0.2 * 20² * 0.5 + 30² * 0.3 - 21² ]

= 7

b)

Mean = $\sum$ X * P(X)

= 1 * 0.4 + 3* 0.20 + 5 * 0.1 + 7 * 0.3

= 3.6

Standard deviation = sqrt [ $\sum$ X² * P(X) - Mean² ]

= sqrt [ (1² * 0.4 + 3²* 0.20 + 5² * 0.1 + 7² * 0.3 - 3.6² ]

= 2.5377