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abc4616

Member

Registered: 2006-10-01

Posts: 9

Mean and Variance Question

If a random variable X is defined such that E[(X-1)^2]=10 and E[(X-2)^2]=6, find the mean and variance of X.

Does anyone know how to approach this question??

Here is what I got so far:

E[(X-1)^2]=10 : E(X^2) - 2E(X) + 1= 10
E[(X-2)^2]=6: E(X^2) - 4E(X) + 4= 6

What should I do next to get the mean and variance?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Mean and Variance Question

You're almost there already. You have:

E(X²) - 2E(X) +1 = 10
E(X²) - 4E(X) +4 = 6

Taking the second from the first gives 2E(X) - 3 = 4
Therefore, 2E(X) = 1 and so E(X) = 0.5, which is the mean.

Now you know E(X), you can substitute it into one of the original equations to find E(X²).

E(X²) - 2*0.5 + 1 = 10, so E(X²) = 10.

The variance is given by E(X²) - E(X)², and so the variance is 10-0.5² = 9.75.

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