Question

The random variable X is exponentially distributed, where X represents the waiting time to see a shooting star during a meteor shower. If X has an average value of 49 seconds, what are the parameters of the exponential distribution

Answer 1

`X \sim Exp (\mu = 49)`

But also we can define the variable in terms of
`\lambda` like this:

`X \sim Exp(\lambda= (1)/(\lambda) = (1)/(49))`

And usually this notation is better since the probability density function is defined as:

`P(X) =\lambda e^(-\lambda x)`

Explanation:

We know that the random variable X who represents the waiting time to see a shooting star during a meteor shower follows an exponential distribution and for this case we can write this as:

`X \sim Exp (\mu = 49)`

But also we can define the variable in terms of
`\lambda` like this:

`X \sim Exp(\lambda= (1)/(\lambda) = (1)/(49))`

And usually this notation is better since the probability density function is defined as:

`P(X) =\lambda e^(-\lambda x)`