Let x be a random variable with mean x = 25 and x = 6 and let y be a random variable with mean y = 30 and y = 4. it is known that x and y are independent random variables. suppose the random variables x and y are added together to create new random variable w (i. e., w = x + y). what is the standard deviation of w?

I'm guessing you intended to say has mean and standard deviation , and has means and standard deviation .

If , then has mean

and variance

Given that and , we have

Then

and are independent, so , and

so that the variance, and hence standard deviation, are

# # #

Alternatively, if you've already learned about the variance of linear combinations of random variables, that is

then the variance of is simply the sum of the variances of and , , and so the standard deviation is again .

answer: #1 ads up by 8 and i don't know #2