Final answer:
The statement that (Y₁, Y₂, Y₃) denote a random sample from an exponential distribution is true, concerning the mean of the sampling distribution. Also, the exponential distribution could be used as the testing distribution in hypothesis tests, depending on the specifics of what is being tested.
Step-by-step explanation:
The question asks whether it is true that (Y₁, Y₂, Y₃) denote a random sample from an exponential distribution with density function (f(y)). The answer provided to this is 'True.' The mean of a sampling distribution of the means is generally equal to the mean of the data distribution, according to the Central Limit Theorem, as long as the sample size is sufficiently large. This is true for any distribution, not just the exponential distribution. When dealing with exponential distributions, this property holds as well, assuming that the sample size is large enough to invoke the approximation provided by the Central Limit Theorem.
Conducting hypothesis tests with exponential distributions would involve using the correct distribution for the test. It is true that if you are dealing with the sum of exponential random variables, the sum tends to approximate a normal distribution as the sample size increases, which is seen in part i of the information. The keyword 'B exponential' suggests that the testing distribution for the hypothesis mentioned could be the exponential distribution, depending on the context of the hypothesis being tested.