1.  Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are two hypotheses on the expected value: H1: E[X(t)] = l₁t = 80t and H2: E[X(t)] = l₂t = 85t. We will use t = 30 in this question and suppose the number of calls received is 2475.

For a value a of significance level, there are four possibilities for accepting / rejecting the hypotheses: H1 and H2 both accepted, H1 and H2 both rejected, H1 accepted and H2 rejected, H2 accepted and H1 rejected.

1. Find / compute a significance level a (a = ?) that both H1 and H2 are accepted (show the calculation) or explain why such significance level does not exist.
2. Find / compute a significance level a that both H1 and H2 rejected (show the calculation) or explain why such significance level does not exist.
3. Find / compute a significance level a that H1 is accepted and H2 is rejected (show the calculation) or explain why such significance level does not exist.
4. Find / compute a significance level a that H2 is accepted and H1 is rejected (show the calculation) or explain why