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## Homework Statement

X is exponentially distributed. 3 observations are made by an instrument that reports x1=5, x2=3, but x3 is too large for the instrument to measure and it reports only that x3 > 20 . (The largest value the instrument can measure is 10)

a)What is the likelihood function?

b)What is the mle of t?

## Homework Equations

f(x;t)=t*exp(-t*x), E(X)=1/t ,

F(x) = P(X<=x)=1-exp(-t*x)

## The Attempt at a Solution

a)(t^3)*exp(-3t*(avg of X))

b) take natural log of a), take derivative, then set equal to 0 and solve for t

Wondering if I am on the right track?

Thanks