Suppose a research paper states that the distribution of the

Suppose a research paper states that the distribution of the daily sea-ice advance/retreat from each sensor is similar and is approximately double exponential. The proposed double exponential distribution has density function f(x) = 0.5e^(|x| )for < x < . The standard deviation is given as 41.8 km. (Round your answers to four decimal places.)

(a) What is the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value?

Solution

In the bilateral exponential distribution, variance is 2/², so the standard deviation is 2/. In this case, 40.9 = st. dev. = 2/, so = 2/41.8 = 0.0338.

(a) The P[0 < x < something] for the bilateral exponential is half of P[0 < x < something] for the exponential, and the distribution is symmetric. So:

P[-41.8 < x < +41.8] = 2 * (1/2) P[x < 41.8] = 1 - e^-41.8 = 1 - e^{-41.8(0.0338)} = 1 - 0.2435 = 0.7565