Suppose that w1, w2, and w3 are independent uniform random variables with the following distributions: wi ~ uni(0,10*i). what is the standard deviation of w1+w2+w3? using r, compute this value. round the answer to 2 decimal places and enter into the box:

I'll leave the computation via R to you. The are distributed uniformly on the intervals , so that

each with mean/expectation

and variance

We have

so that

Now,

and

We have

because and are independent when , and so

giving a variance of

and so the standard deviation is

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

and since the are independent, each covariance is 0. Then

and take the square root to get the standard deviation.

it is probably the graph on the bottom right.

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