1. A discrete random variable X has possible values 0, 1, 2, 3, 4, 5, 6, 7, 8 with the following partial probability distribution. The missing probabilities P(X = 7) and P(X = 8) are equal to each other. X 0 1 2 3 45678 P(X=x) 0.04 0.06 0.11 0.12 0.14 0.17 0.2 NA Put the values x = 0:8 and the tabled probabilities p into a data frame (use tibble()). Write code to calculate the missing values for P(X = 7) = P(X = 8) and replace the missing. values with these calculated values into your data frame. Verify that the sum of all probabilities is 1. Calculate the mean, variance, and standard deviation of this distribution.