Question

In: Statistics and Probability

We have studied the following notorious continuous distributions:

We have studied the following notorious continuous distributions:

| | | | | -------- | ------- | --------- | ----------------- | ------- | ---------

Normal | Beta | Weibull | Exponential | Lognormal | Uniform (continuous)

Based on the following scenarios and descriptions, name which distribution would be your "go-to" for modeling the following quantities.

* The time left on a 15 second radio ad when you turn on a radio and an ad happens to be on.

**Response:**

* The length of time between power outages at your home. Studies show that the probability per unit time of this occurring is relatively constant, and expected time until the next outage is independent of how long the power has already continuously been on.

**Response:**

* The proportion of the original meal's weight that ends up on the floor when a baby eats a meal.

**Response:**

* The difference in what a person weighs today vs. what they weighed yesterday.

**Response:**

* The amount of loans that students nationwide take out to pay for college (among people who have to take out at least one loan).

**Response:**

* Daily amount of data used by subscribers to Comcast (skewed right).

**Response:**

* The lengths of people's index fingers.

**Response:**

* The distance a person can walk a continuously increasing incline before feeling winded (skewed left).

**Response:**

* The proportion of household incomes that go toward bills.

**Response:**

Solutions

Expert Solution

Uniform:The ad is played for 15 minutes Let X be the time left for the ad between 0 and 15 minutes

Exponential :explained aboove is the lack of memory property of exponential distribution. Here X be the time between two outages

Beta: the random variable takes value betwwen 0 and 1. Since proportion of orginal meals weight that ends up on floor takes value between 0 and 1

Normal:The difference is tge successive weights normally 0 and most of the time differences cluster around zero which is the mean value here is a property of normal distribution

Log normal: The data on the amount of loan is skewed to the right... So such data can easily be made normal by taking logarithm... Hence the original is lognormal

Lognormal: same arugument as above daily suscribers is also right skewed

Normal:peoples index fingers will not vary much in their lengths... In most of the cases the observations are normal

Weibul:the length of walk can be correlated with the life length of a bulb..we know weibul diatribution is mainly known for its application as a life time distribution..

Beta:proportion again can take any value between 0 and 1...hence the last case of proportion of household incomes can be taken to be following beta distribution


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