discrete probability

[chicklet2386]

Given the following discrete probability distribution, find all possible values of a and b such that the standard deviation is 1.

x 1 2 3 4
p(X=x) 0.2 0.1 a b

Is there a way to compute this by calculator without knowing the mean?

 

[tkhunny]

Calculate the mean using the defintion.

We know: 0.2 + 0.1 + a + b = 1.0

We calculate the mean: 1*0.2 + 2*0.1 + 3*a + 4*b = M

Calculate the second moment: 1*0.2 + 4*0.1 + 9*a + 16*b = R

Calculate the Standard Deviation: sqrt(R - M^2) = 1

Seems like there's enough information to wade through it. Let's see what you get.