At a shop, the price doesn't vary but it varies independently between shops. If I buy two sodas from the same shop what the expected price and standard deviation? If my friend buys two sodas from two different shops what's the expected price and standard deviation?
What I have attempted
I am thinking my expected price is $E(3)+E(3)=\$6.00$ for my expected price of soda,
my standard deviation is: $1^2+1^2=\sqrt 1$ so $1.414$
My friend's is: expected price $E(3)+E(3)=\$6.00$ for her expected price of coffee,
her standard deviation is: $1^2+1^2=\sqrt1$ so 1.414
The prices $\ F_1, F_2\ $ your friend pays for her cups of coffee are independent random variables each with mean $\ \$3\ $ and standard deviation $\ \$1\ $, so the total cost $\ F_1+F_2\ $ she pays will have mean $\ \$6\ $ and standard deviation $\ \$\sqrt{2}\ $, as you have surmised.
The prices $\ Y_1,Y_2\ $ you pay for your cups of coffee, however, are not independent, because $\ Y_2=Y_1\ $. While the total cost $\ 2Y_1\ $ you pay for your cups of coffee also has a mean of $\ \$6\ $, its standard deviation is $\ \$2\ $, not $\ \$\sqrt{2}\ $.