1. Consider a weighted 8-sided die where a die roll of x has probability kx for some k E R. a. Find the value of k to make a valid probability distribution. b. Show the distribution in one of the two...

Extracted text: 1. Consider a weighted 8-sided die where a die roll of x has probability kx for some k E R. a. Find the value of k to make a valid probability distribution. b. Show the distribution in one of the two proper forms С. Calculate the standard deviation of this distribution by hand, correct to 4 decimal places. d. If you and I each roll one of these weighted dice, what is the probability that the sum is 14? e. If you roll this die 9 times, what is the probability of getting a roll of 5 more than two times?