1) A traditional die is a cube with each of its six sides representing the numbers from 1 to 6. Mr. Dicey customized a die by replacing each number with its reciprocal (reciprocal of x is 1/x ). What is the expected value if you roll the customized die for 6 times? 2) A game is played by throwing 3 dice. You will win in this game if the summation of the scores of these 3 dice is 3, 4, 17, 18.

What is the variance of your expected values?

3) Two dice are rolled. [A die has six sides, each representing the score from 1 to 6]

What is the expected value if you roll these two dice for 6 times?

1)

2) 49.225

3)

Step-by-step explanation:

1) To find the expected value of the dice we can use the following equation:

So in our problem the values x will be: 1/1, 1/2, 1/3, 1/4, 1/5 and 1/6 and the probavility for all values is 1/6 so the expected values will be:

2) To find the variance of the expected values we can use the equation:

So for our problem will be:

3) To find the expected value of the dice we can use the following equation:

So in our problem the values x will be: 1, 2, 3, 4, 5 and 6 and the probavility for all values is 1/6 so the expected values will be:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.