Question

Probability And Statistics

Question:

Explain the exponential random variable and normal random variable with at-least ten examples in real life? In which situation we prefer normal random variable instead of exponential variable?

Answer 1

EXPONENTIAL RANDOM VARIABLES: this type of random variables are often used to model waiting times between events. so for instance, when i thaught an undergraduate modeling course, i had one student who went to the mathematics help room and had a stopwatch and kept track of the times between when students would arrive to the center for the help. the histogram of these times looked very close to that of an exponential distribution .(the service times were very different , almost a uniform distrbution.)

more recently , i had a senior thesis student who studied the distribution of performance of baseball players , and found an exponential distribution was a much better fit than other distributions.

More esoterically , one can take data that is streaming from a computer simulation as bernoulli random variables, and by adding in some extra randomness, turn the variables into exactly exponentially distributed random variables. this allow one to get exact extremely high confidence intervals for the output of the simulation . these are much close to truly exponential because they arise from computer simulations where the assumptions such as independent data can be directly enforced.

the amount of money customers spend in one trip to the supermarket follows an exponential distrbution. there are more people who spend small amounts of money and fewer people who spent large amounts of money .

exponential ditribution is widely used in the field of reliability. Reliability deals with the amount of time a product lasts.

NORMAL RANDOM VARIABLES:

thanks a lot