Poisson Process

If two independent Poisson processes with rates λ₁ and λ₂ are merged, what is the rate of the resulting process?
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In a Poisson process with rate λ, if each event is independently classified as Type A with probability p and Type B with 1-p, what is the rate of the resulting Type A process?
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Why is a Poisson process suitable for modeling the emission of radioactive particles?
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In the call center model, if calls arrive following a Poisson process with λ = 10 calls/hour, what is the expected number of calls in a 30-minute interval?

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When splitting a Poisson process, the resulting processes are also Poisson. What property must the splitting mechanism satisfy for this to hold?
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