Events A and B are such that P(A)=0.4, P(B| A)=0.7 and P(ACB)=0.3. (a) Find the values of P(AB) and P(B). (b) (c) Demonstrate, with reasoning, whether A and B are: mutually exclusive, independent. (i) A data set presented in the form of a frequency table is given as below: Frequency 0 1 2 3 4 5 6 7 8 9 10 11 12 Data 2 180 904 7639 19764 22636 23710 23594 44868 57901 11511 83000 393 Table 01(c) (4 marks) (4 marks) formula is in Student canvas. Determine the following quantities for the above data set: (i) Sample size; (ii) Mode; (iii) Median; (iv) (v) Inter-quartile range; (vi) Standard deviation; (vii) Range; If you used Excel/R to aid in the computations, do include screenshots of the software as proof. (12 marks) Mean;