Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows: 1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2

Which of the following statement is correct?

a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one

D is correct

Step-by-step explanation:

Here, we want to select which of the options is correct.

The correct option is the option D

Since the die is unfair, we expect that the probability of each of the numbers turning up

will not be equal.

However, we should also expect that if we add the chances of all the numbers occurring together, then the total probability should be equal to 1. But this does not work in this case;

In this case, adding all the probabilities together, we have;

1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/2

= 5(1/12) + 1/2 = 5/12 + 1/2 = 11/12

11/12 is not equal to 1 and thus the probability distribution cannot be correct

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

mia khalifa

step-by-step explanation: