Determine the laplace transform of the probability , Mathematics

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1. Let ,

637_sigma.pngwhere  are independent identically distributed random variables according to an exponential distribution with parameter μ. N is a Binomially distributed random variable with success probability p. Determine the Laplace transform of the probability distribution of the random variable Y.

2. Given a Poisson arrival process with parameter λ, determine the distribution of the number of arrivals during an exponentially distributed time interval with parameter  μ.

 

 


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