Question

L.11) Brand name distributions a) Give an example of a normally distributed random variable. b) Give an example of an exponentially distributed random variable. c) Give an example of a random variable with the Weibull distribution. d) Give an example of a random variable with the Pareto distribution.

Answer 1

a) Distribution of blood pressure is  approximately a normal distribution with mean 85 mm. and standard deviation 20 mm. If we draw a histogram of 30 and more observation we will get a bell- shape curve in which  68% of the observations lying within one standard deviation of the mean, 95% within two standard deviations and 99.7% within 3 standard deviations.

b) The time between successive events has exponential distribution, telephone calls during a fairly short time period or people arriving in a bank queue at lunchtime or the life time of electronic components, i.e., an inter failure time are the examples of exponential distribution

c) In weather forecasting ,the distribution wind speed often matches the Weibull shape. Weibull distribution is also applied to extreme events such as annual maximum one-day rainfalls and river discharges.

d) Pareto distribution majorly used to describe the allocation of wealth among individuals, it shows the way that a larger portion of the wealth of any society is owned by a smaller percentage of the people in that society.