Mathematics: 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?

The random variable X is exponentially distributed,

Hannahrose911

14.02.2022

The parameters of the exponential distribution is 0.0133.

Step-by-step 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:

$\theta=\frac{1}{\mu}\\\\$

$=\frac{1}{75}\\\\=0.013333333333\\\\\approx 0.0133$

Thus, the parameters of the exponential distribution is 0.0133.

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