Unstable particles are emitted from a source and decay at a distance

X, which is exponentially distributed with unknown parameter (J. A special device is

used to detect the first n decay events that occur in the interval [ml , m2j . Suppose

that these events are recorded at distances X = (XI , ... , Xn).

Problem 5. Unstable particles are emitted from a source and decay at a distance X, which is exponentially distributed with unknown parameter 0. A special device is used to detect the first n decay events that occur in the interval [m1, my]. Suppose that these events are recorded at distances X = (X1, . .., Xn). (a) Give the form of the likelihood and log-likelihood functions. (b) Assume that mi = 1, m2 = 20, n = 6, and r = (1.5, 2, 3, 4,5, 12). Plot the likeli- hood and log-likelihood as functions of 0. Find approximately the ML estimate of e based on your plot