Likelihood Function - Exponential Distribution

[Merka]

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

 

[ToxicBug]

I've answered your other topic.