Question about Standard Deviation

Question

x	P(x)
0	0.05
1	0.3
2	0.3
3	0.35

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

  

Answer 1

x_avg = sum from x = 0 to 3 of xp(x) = 0(.05)+1(.3)+2(.3)+3(.35) = 2.25

variance = sum from x = 0 to 3 of (x-x_avg)²p(x)

= .05(-2.25)² +(-1.25)²(.3)+(-.25²(.3)+(1.25²(.35) = 1.29

stand. dev = sqrt(var) = 1.135