a The number N(t) of bubbles in a fizzy drink decreases with time t according to a continuous- time Markov process. Duri
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a The number N(t) of bubbles in a fizzy drink decreases with time t according to a continuous- time Markov process. Duri
a The number N(t) of bubbles in a fizzy drink decreases with time t according to a continuous- time Markov process. During any short interval between times t and t + h, the number N(t) decreases by 1 with probability dhN(t), where d is some constant. (a) By considering Pn(t+h), the probability of having n bubbles at time t+h, derive the governing differential equation for Pn(t). (b) If there are no bubbles initially, what is the probability of having the same number of bubbles after time t?
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