Answer:
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
