Question

A continuous random variable X denote the time between detection of a particle with a Geiger counter. The probability that we detect a particle within 30 seconds of starting the counter is 0.50.

The random variable X has the "Lack of memory" property that After waiting for three minutes without a detection, the probability of a detection in the next 30 seconds is the same as the probability of a detection in the 30 seconds immediately after starting the counter.

What is the name of the probability distribution does X follow?

Group of answer choices

X follows Gamma Distribution.

X follows Exponential Distribution.

X follows Binomial Distribution.

X follows Poisson Distribution.

Answer 1

The correct option is the second option: X follows Exponential Distribution. [ANSWER]

Explanation:

We are given that the distribution of X is a continuous and that it possesses the "Lack of memory" property. We know that the exponential distribution is the only continuous distribution with the "lack of memory" property, thus we can conclude that X follows Exponential Distribution and the correct option is the second option.

First option is not correct because the Gamma distribution does not possess the "lack of memory" property.

Third and fourth options are not correct because Binomial and Poisson distribution are discrete distributions whereas X is a continuous random variable.

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