Applying Linear Functions to a Random Sequence
3 points possible (graded)
Let (Zn)n≥1 be a sequence of random variables such that
n−−√(Zn−θ)−→−−n→∞(d)Z
for some θ∈R and some random variable Z.
Let g(x)=5x and define another sequence by Yn=g(Zn).
The sequence n−−√(Yn−g(θ)) converges. In terms of Z, what random variable does it converge to?
n−−√(Yn−g(θ))−→−−n→∞(d)Y.
(Answer in terms of Z)
Y=