Let X1 XN be a random sample from a population with pmf Le

Let X₁, ... , X_N be a random sample from a population with pmf:

Let X1, ... , XN be a random sample from a population with pmf: Theta? 0 leq Theta leq 1/2 What is the MLE of x = 1, x = 0 or P_Theta (X = x) = (1-Theta )^1^-^xTheta ^x,

Solution

Total prob = (1-t)+1(t) = 1

Theta lies between 0 and 1/2

From the prob we see that theta and 1-theta can be interchanged

i.e. if theta 1 = 1-theta

then P(X=x)= theta1^x(1-theta1)^1-x

Thus as theta = 1-theta1 give the same function

solving we get theta = 1/2

MLE of theta = 1/2