Final answer:
The variance of an exponential random variable is the reciprocal of the square of its decay parameter. Without the decay parameter provided, we cannot determine the correct answer from the provided options. Nonetheless, if we assume a decay parameter of 0.2, the variance would be 25, corresponding to option 4.
Step-by-step explanation:
The question asks about the variance of an exponential random variable y. An exponential distribution is described by its decay parameter m, and the variance of an exponential distribution is the reciprocal of the square of its decay parameter. Given that the average length of a phone call, which is an exponential random variable, is equal to 8 minutes, we can define the decay parameter m as 1/8. Therefore, the variance of this exponential random variable is (1/m)^2 = (1/(1/8))^2 = 8^2 = 64. However, since this number isn't among the provided options, it is possible that the question is missing crucial information, or there may be a misunderstanding in the formulation. If instead the decay parameter m were given as 0.2, as seen in the related content, the variance would then be (1/0.2)^2 which equals 25. This aligns with option 4 given in the question