Sample mean and sample standard deviation for the given data set.
The number of spaces, X, one moves ones token when playing a certain board game is determined by using a spinner board marked off into three circular sectors : a sector corresponding to is 240° wide, a sector corresponding to is 90° wide, and a sector corresponding to ' is 30° wide.)
(a) Find E[X] = µ_{x} and Var[X] = µ_{x}^{2}.
(b) The designers of the game did 600 spins of the game spinner and obtained the following results
Spaces

Frequency

3

402

8

147

12

51

Find out the sample mean and sample standard deviation for number of spaces moved.
(c) Under certain special conditions, a player is allowed to move a certain number of extra spaces. The number of extra spaces, Y, is determined by flipping a coin: if the coin comes up tails the number of extra spaces one moves is 2; if the coin comes up heads the number of extra spaces is 4.
If W denotes the total number of spaces one moves under these special conditions, find out the mean and standard deviation of W.