Let T1,T2,…,Tn be i.i.d. observations, each drawn from a common normal distribution with mean zero. With probability 1/2 this normal distribution has variance 1, and with probability 1/2 it has variance 4. Based on the observed values t1,t2,…,tn, we use the MAP rule to decide whether the normal distribution from which they were drawn has variance 1 or variance 4. The MAP rule decides that the underlying normal distribution has variance 1 if and only if

∣∣∣c1∑i=1nt2i+c2∑i=1nti∣∣∣<1.
Find the values of c1≥0 and c2≥0 such that this is true. Express your answer in terms of n, and use 'ln' to denote the natural logarithm function, as in 'ln(3)'.

c1=- unanswered
c2=0 - unanswered
0

6 answers

c2 = n*ln(1)

please! if you are reading this, be generous and provide your answers for the whole problem set
@RVE, do you know what c1 is equal to? I'm still having trouble with this problem.
anyone know what is c1?
Any clue how you got the term ti, I'm getting only ti^2
Since we are trying to determine variance should it be assumed to be discrete measurement based on continuous observation?
C1: 3/(8*n*ln(2))
C2: n*ln(1)