uniform distribution of random independent variables

okay. my exam is approaching in a few days and I have one last question.

Let X1, X2, ... X7 be a set of seven independent random variables, each

having the uniform distribution of values from the [3, 6] interval (this is

called random independent sample of size 7 from this distribution).

(a) Find the expected value and standard deviation of their sum T ≡ X1 + X2 + ... + X7.

(b) What is the probability that more than three of these seven random

variables will have a value smaller than 1

3?

(c) Find the skewness and kurtosis of X1.

__answers:__

(a) E(x) = 7(6+3)/2 = 31.5

Var(x) = 7*[(6-3)^2]/2

standard deviation = 2.2913

(b) not sure

(c) would skewness be 0 since its uniform? what about kurtosis