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.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

the first option is the answer.