1. ## a log-likelihood problem

$X_i$ for $i=0,\dots,n$ are from Exponential distribution

$X_1,\dots,X_m$ are observed

$X_{m+1},\dots,X_n$ are censored at $\tau$
i.e. they have the cumulative distribution function $F(\tau,\theta)=P(X_i \leq \tau)$

likelihood is given by
$\prod_{i=1}^m f(x_i;\theta)\prod_{i=m+1}^n (1-F(\tau,\theta))$

how do i show that the complete data log-likelihood is a linear function of $x_{m+1},\dots,x_n$

Thanks.

casper