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

Question

∣∣∣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

Answer 1

c2 = n*ln(1)

please! if you are reading this, be generous and provide your answers for the whole problem set

Answer 2

@RVE, do you know what c1 is equal to? I'm still having trouble with this problem.

Answer 3

anyone know what is c1?

Answer 4

Any clue how you got the term ti, I'm getting only ti^2

Answer 5

Since we are trying to determine variance should it be assumed to be discrete measurement based on continuous observation?

Answer 6

C1: 3/(8*n*ln(2))
C2: n*ln(1)