I need in depth explanation. thank you so much.

2) Suppose an experiment consits of rolling a fair six sided die once. Let x be the random variable that counts the number of dots showing on the die. Complete the following: [2 marks each] a) Define a probability function f(x) for the experiment. b) Find the expected value E(x) = / c) Find the variance Var(x) = q2 d) Find the standard deviation o e) Plot the graph of the probability function. f(x) 0.20- 0.15- Probability 0.10- 0.05- 0.00+ Number of dots