Describe the distribution where radioactive particles are emitted at a poisson rate of 5 per second. Let W reflect the waiting time until the 20th particle. What is the expected time here?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Describe the distribution where radioactive particles are emitted at a poisson rate of 5 per second. Let W reflect the waiting time until the 20th particle. What is the expected time here?
From the given information,
Consider,
X is the random variable that represents the waiting time until the first particle is emitted.
where radioactive particles are emitted at a Poisson rate of 5 per second. That is,
Thus,
It has been given that X (in seconds) ~ Exponential(λ = 1/5).
Therefore, the cumulative distribution function of X is as given below:
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