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Exponential distribution hypothesis testing

I have to show the size of a test is a=1/3

X is a random sample of size 1 from exp distribution.
Null hypothesis ho = 1/2 rejected in favour of h1 = 1
If f(x;1/2)/f(x;1) <= 3/4

Thanks for any help I don't understand how you would do the exponential as its not in tables

Reply 1

ghostwalker

Original post by chloeaj95

You have the pdf

\lambda e^{-\lambda x}

, so plug that in to your rejection criterion to work out the range of x.

Then use that range to work out the probability.

Also, I'd work with exact values.