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

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walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.