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
(c) Find the skewness and kurtosis of X1.
(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
this is the one thing we were given about for kurtosis, part of our exponential stuff (not uniform like the question asks)
[E(X4)−4μE(X3)+6μ2E(X2)−3μ4]/σ4 = ...
[24β4−4×6β4+6×2β4−3β4]/β4 = 9
does this help at all? if not, ill just hope this specific type of question doesnt make its way to the exam