Give three examples of Bernoulli rv's (other than those in the text). (Select all that apply.) X = the number of days in year where the high temperature exceeds 100 degrees and X = 0 if there are none. X = 1 if a randomly selected shopper purchases a food item at a deparment store and X = 0 otherwise. X = 1 if a randomly selected day has a high temerpature of over 100 degrees and X = 0 otherwise. X = the number of lightbulbs that needs to be replaced in a randomly selected building and X = 0 if there are none. X = 1 if a randomly selected lightbulb needs to be replaced and X = 0 otherwise. X = the number of food items purchased by a randomly selected shopper at a deparment store and X = 0 if there are none.

Step-by-step explanation:

A bernoulli variable random variable can only take 2 possible values: 0 and 1. Examples of bernoulli random variables are

1) We throw a dice, if the result is an even number, then X = 1, otherwise, X = 0.

Even though the dice itself has 6 possible result, the result has only two possibilities: be even or be odd. Thus, X is bernoulli.

2) Team A play vs Team B in a soccer match. If Team A wins, then X = 1, if there is a draw or Team B wins, then X = 0.

Here we are evaluating between 2 possibilities: whether team A wins or not, so we have only two possible values for X: 0 and 1, thus it is bernoulli. Even though there are 3 possible results in a soccer match, the value of X doesnt distinguish between Team B victory and a draw, thus, we have only two relevant results for X.

3) X = 1 if a during a randomly selected day it rains and X = 0 if that is not the case.

Again, X has two possible results, thus it is Bernoulli.

Now, lets see the ones given in the text:

X = the number of days in year where the high temperature exceeds 100 degrees and X = 0 if there are none

This is not a random variable becuase X can take any value from 0 to 365 as long as it is integer.

X = 1 if a randomly selected shopper purchases a food item at a deparment store and X = 0 otherwise

Since X can only take the values 0 and 1, then this is bernoulli.

X = 1 if a randomly selected day has a high temerpature of over 100 degrees and X = 0 otherwise

This is another example of a bernoulli random variable, since it can take only the values 0 and 1

X = the number of lightbulbs that needs to be replaced in a randomly selected building and X = 0 if there are none

This is not a bernoulli random variable because X can take any integer bigger than or equal than 0

X = 1 if a randomly selected lightbulb needs to be replaced and X = 0 otherwise

Observe that if we select just 1 ligthbulb, then it can either need to be replaced or not, so there are just 2 possibilities: this variable is bernoulli.

X = the number of food items purchased by a randomly selected shopper at a deparment store and X = 0 if there are none

Again, X can take any value bigger than or equal to 0, so X is not bernoulli