Homework Statement
Homework Equations
The Attempt at a Solution
this isn't really homework, but I was just wondering if someone could offer an intuitive reason as to why when random variables are transformed, we use absolute values of derivative of those functions, as opposed...
Homework Statement
Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2.
Homework Equations
Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...
Homework Statement
Suppose that X1 and X2 have the joint pmf
f(x_{1},x_{2})=p^{2}q^{x_{2}},x_{1}=0,1,2,...,x_{2},x_{2}=0,1,2,...
with
0<p<1,q=1-p
Homework Equations
The Attempt at a Solution
I'm confused because the expression doesn't have x_1 in it. So usually, if I want to...
Homework Statement
For any cdf F(x) of a continuous random variable, show that
\int_{-\infty}^{\infty}[F(x+b)-F(x+a)]dx=b-a
for any a<b.
Homework Equations
The Attempt at a Solution
Not really sure where to begin. I figure I can split the integrals and do u subs, and (after...