Question

Let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes. If the random variable X is known to be exponentially distributed, what are the parameters of this exponential distribution

Answer 1

Answer:

The parameters of this exponential distribution is $\lambda$ = $\frac{1}{27}$ .

Step-by-step explanation:

We are given that the random variable X is known to be exponentially distributed and let X be the time it takes for a person to choose a birthday gift, where X has an average value of 27 minutes.

So, X = time it takes for a person to choose a birthday gift

The probability distribution function of exponential distribution is given by;

 $f(x) = \lambda e^{-\lambda x} , x >0$      where, $\lambda$ = parameter of distribution.

Now, the mean of exponential distribution is = $\frac{1}{\lambda}$  which is given to us as average value of 27 minutes that means  $\lambda = \frac{1}{27}$ .

So, X ~ Exp( $\lambda = \frac{1}{27}$ ) .

Therefore, the parameter of this exponential distribution is $\lambda$ .