A wireless pressure sensor (buried in the ground) reports a discrete random variable X with range SX = {1,2,..., 20} to signal the presence of an object. Given an observation X and a threshold x0, we decide that an object is present (hypothesis H1) if X > x0; otherwise we decide that no object is present (hypothesis H0). Under hypothesis Hi, X has conditional PMF

where p0 = 0.99 and p1 = 0.9. Calculate and plot the false alarm and miss probabilities as a function of the detection threshold x0. Calculate the discrete receiver operating curve (ROC) specified by x0.

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(1-pp-1 1-P 0 otherwise,