Question

The time t (in minutes) spent at a driver's license renewal center is exponentially distributed with a mean of 35 minutes. Exercise (a) Find the probability density function of the random variable t. The exponential probability density function f(t) = ae^-at has the mean mu = which means that a =. Exercise (b) Find the probability that t is within one standard deviation of the mean. To find the probability that t is within one standard deviation of the mean, we need to calculate P(mu - sigma

Answer 1

The Probability density function of random variable t is f(x) = 0.0285 e^-(0.0285t)

Exponential Distribution often concerned with the amount of time until some specific event occurs. The exponential distribution is widely used in the field of reliability. Reliability deals with the amount of time a product lasts.

According to the question,

Time spent at center follows exponential distribution with mean 35

Probability density function : $f(t) = ae^{-at}$

Given, mean :μ = 35

a = 1 / mean

=> a = 1 / 35  => 0.0285

So, the pdf : f(x) = 0.0285 e^-(0.0285t)

To find probability that t is within one standard deviation of mean = P( μ - σ < t < μ+σ) ,  first we need to calculate variance

Variance : σ = (mean)²

=> σ = 35²

=> σ = 1225

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