Final answer:
The statement in the question is true. If a random variable does not converge in probability, the conditional expectation of the random variable also does not converge.
Step-by-step explanation:
The statement in the question is true. If a random variable does not converge in probability, it means that the probability of the random variable approaching a certain value is not getting closer to 1 as the number of trials increases. If the conditional expectation of the random variable converges, it means that the expected value of the random variable, given a certain condition, approaches a certain value as the number of trials increases.
Since the random variable does not converge in probability, it also means that the expected value of the random variable does not converge.