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

Answer:

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

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

$X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})$

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

$P(X) =\lambda e^{-\lambda x}$

Step-by-step 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:

$X \sim Exp(\lambda= \frac{1}{\lambda} = \frac{1}{49})$

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

$P(X) =\lambda e^{-\lambda x}$