How do I find the standard deviations of the random variables in this chart (a and b are separate)?

Question

anonymous · Answer

attachment

anonymous · Answer

what is a standard deviation of a random variable?

anonymous · Answer

You can find the standard deviation by first getting the arithmetic mean:
$$mean = \frac{ 1 }{ N }\sum_{i = 1}^{N}x _{i}$$
Then you can find the standard deviation from the mean:
$$STD Dev =\sqrt{\frac{ 1 }{ N-1 }\sum_{i = 1}^{N}(x _{i }- mean)^{2}}$$

anonymous · Answer

oh it is the square root of the variance

jim_thompson5910 · Answer

Mean: 

$$\Large \mu = \sum_{i = 1}^N x_i*p_i$$

the mean is also called the "expected value" E(x)

anonymous · Answer

expected values of the first one is 
$$10\times .3+20\times .3+30\times .2$$

jim_thompson5910 · Answer

the standard deviation is given here (along with the mean as well) https://onlinecourses.science.psu.edu/stat200/node/36

anonymous · Answer

damn typo $$10\times .3+20\times .5+30\times .2$$ does that look right @jim_thompson5910

jim_thompson5910 · Answer

yeah for part a), looks good

anonymous · Answer

here is a really nice worked out example we can copy it if you like http://nzmaths.co.nz/category/glossary/standard-deviation-discrete-random-variable

anonymous · Answer

$$E(X)=10\times .3+20\times .5+30\times .2=19$$if my arithmetic is correct 
now we need $$E(x^2)$$

anonymous · Answer

$$E(X^2)=10^2\times .3+20^2\times .5+30^2\times .2=410$$

anonymous · Answer

then your answer is 
$$\sigma = \sqrt{410-19^2}$$ please someone check this

jim_thompson5910 · Answer

I'm getting sigma = 7 as well

jim_thompson5910 · Answer

this calculator is handy to check http://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php