An exponential random variable has a standard deviation of 16. Calculate The probability that it takes on a value < 11. Use 3 decimal places.

And using the cdf we got:

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

And 0 for other case. Let X the random variable that represent the random variable of interest and we know that the distribution is given by:

We know the variance on this case given by :

So then the deviation is given by:

And if we solve for we got:

The cumulative distribution function for the exponential distribution is given by:

Solution to the problem

And for this case we want to find this probability:

And using the cdf we got:

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !