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 75 seconds, what are the parameters of the exponential distribution?

Answer 1

The parameters of the exponential distribution is 0.0133.

Explanation:

Exponential distribution is a continuous probability distribution.

The density function of exponential distribution is,

`f _(X)(x)=\theta \cdot e^(-\theta\cdot x),\ x\geq 0`

Here the parameter θ is the reciprocal of the mean of the random variable X.

The random variable X has an average value of 75 seconds.

Compute the parameters of the exponential distribution as follows:

`\theta=(1)/(\mu)\\\\`

`=(1)/(75)\\\\=0.013333333333\\\\\approx 0.0133`

Thus, the parameters of the exponential distribution is 0.0133.