A public speaker computes the probabilities for the number o

A public speaker computes the probabilities for the number of speeches she gives each week C the mean, variance, and standard deviation of the distribution shown below: If she receives $2500 per speech, how much will she cam per week?

Solution

Consider:

Thus,  
  
E(x) = Expected value = mean =    2 [ANSWER]

Var(x) = E(x^2) - E(x)^2 =    1.58 [ANSWER, VARIANCE]

s(x) = sqrt [Var(x)] =    1.256980509 [ANSWER, STANDARD DEVIATION]

**********************

Expected income = 2500*E(x) = 2500*2 = $5000 per week [ANSWER]
  

x	P(x)	x P(x)	x^2 P(x)
0	0.06	0	0
1	0.38	0.38	0.38
2	0.26	0.52	1.04
3	0.13	0.39	1.17
4	0.14	0.56	2.24
5	0.03	0.15	0.75