Use the geometric mean for right triangles here. Like this 
. Cross multiply to get 
, and 
. That simplifies down to 
. Pull out the 9 as a perfect square of 3 and you're left with 
, first choice above.
Use function notation to represent each statement. Six hours after it started raining, the amount of rain was 37 millimeters.
1 answer:
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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.