I have been asked to write down the likelihood function for θ based upon the four given independant tests and then find the value of θ which maximises this function.
I understand how to find what value of θ maximises a function. However, am unsure of how to work out what the function is from the description.
The question in full is as follows:
Suppose that regular light bulbs and long life light bulbs are being tested. The lifetime of regular light bulbs has an exponential distribution with mean θ and the lifetime of long life light bulbs has an exponential distribution with mean 4θ. THe company that manufactures these bulbs intends to measure the lifetimes of two regular (X1,X2) and two long life (Y1, Y2) bulbs. Write down the likelihood function for θ based upon these four given independant tests. What value of θ maximises this function?
Can someone please help to work this out?
Thanks for any help