A set of 40 radioactive decays were observed at various times t given in the following list: {4.99, 4.87, 2.59, 3.04, 3.39. 6.20, 10.61, 7.64, 3.92, 5.33, 4.35, 2.39, 4.16, 6.?4, 3.53, 5.86, 5.41, 26.25, 4.40, 10.29, 2.08. 2.86, 33.92, 3.03, 0.98, 5.63, 4.89, 2.26, 10.49, 6.51, 7.36. 2.13. 6.45. 2.29. 21.15. 4.07, 4.34. 5.38. 169. 4.93}. a) Assuming an exponential decay, that is NH) 0: exp(2. t}, obtain the decay con- stant A and its error using the maidrnum-likelihood method. Is the hypothesis of an exponential decay compatible with the data? b} The data can be grouped as in the following table. Decay time interval [min] Number ofdacays on: 5 21 5 to 10 13 10 to 15 3 Determine the decay constant .1 and its error using the least-squares method. Compare the results with the values from the rst part of the exercise