# Variance and standard deviation of probability distribution

What is the variance of this probability distribution? Round your answer to 3 decimal places. X 1.02 2.04 3.07 4.11 P(X) 0.24 0.25 0.28 0.23 Could you please break down. I also need to know how to get the standard deviation. Thank you for any help given.

• Do you know the formula for the variance of a distribution? Sep 25, 2014 at 23:54
• yes and I have work it over and over. The mean is 2.56
– barb
Sep 26, 2014 at 1:25
• and then I tried to work the formula. I do not know how to put the formula on here. As you can tell I am new at this.
– barb
Sep 26, 2014 at 1:28

## 1 Answer

\begin{align} Var(X)&=E(X^2)-E(X)^2\\ &=(1.02^2\times0.24+2.04^2\times0.25+3.07^2\times0.28+4.11^2\times0.23)-(1.02\times0.24+2.04\times0.25+3.07\times0.28+4.11\times0.23)^2\\ \end{align}

For part 2, look up "standard deviation" and "variance".

• This is how I did it
– barb
Sep 26, 2014 at 14:10
• I got ans. as 1.26 but it is wrong the book says it is 1.429. The mean is 2.56 = 6.554 and then I got 7.814 for the second part and when I subtract I get 1.26
– barb
Sep 26, 2014 at 14:14
• Slight correction Sep 26, 2014 at 22:04