Detection of radioactive elements. you observe particles emitted from a radioactive sample. your task is to determine whether the sample is composed of an element a or of an element b. it turns out that the emission patterns of these two elements are well approximated by independent poisson processes with parameters (or rates as we say) a and b, respectively. from past data you also know that element a is roughly twice as common as element b. as a result, the number of emitted particles at time t can be modeled by