Let X ~ exp(λ)
MGF of X = λ/(1-t)
a) What is MGF of Y = 3X
b) Y has a common distribution, what is the pdf of Y?
c) Let X1,X2,....Xk be independent and identically distributed
with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below
the summation symbol, and k is on top of the summation symbol).
What is the MGF of S?
d) S has a common distribution. What is the pdf of...
The curried version of let f (x,y,z) = (x,(y,z)) is
let f (x,(y,z)) = (x,(y,z))
Just f (because f is already curried)
let f x y z = (x,(y,z))
let f x y z = x (y z)
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}.
a) Prove or disprove: A ⊆ X
b) Prove or disprove: X ⊆ A
c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y )
d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let X and Y be independent and identical uniform distribution on
[0, 1]. Let Z=min(X, Y). Find E[Y-Z].
Hint: condition on whether Y=Z or not. What is the probability
Y=Z?
Let X ∼ Normal(μ = 20, σ2 = 4).
(a) Give the mgf MX of X.
(b) Find the 0.10 quantile of X.
(c) Find an interval within which X lies with probability
0.60.
(d) Find the distribution of Y = 3X −10 by finding the mgf MY of
Y