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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: