Question

Kenyan revenue authority has realised that the annual proportion of erroneous tax returns filled with it is found to be a random variable having a beta distribution with alpha=7 and beta =12 . determine the mean of erroneous tax

Answer 1

The mean of erroneous tax returns is approximately 0.3684. The mean of erroneous tax returns, modeled by a beta distribution with alpha = 7 and beta = 12, is approximately 0.3684.

Step-by-step explanation:

The mean of a beta distribution can be calculated using the formula:

Mean = alpha / (alpha + beta)

In this case, alpha = 7 and beta = 12. Plugging in these values, we get:

Mean = 7 / (7 + 12) = 7 / 19 ≈ 0.3684

Therefore, the mean of erroneous tax returns is approximately 0.3684.

The mean of a beta distribution, denoted by the parameters alpha and beta, is a measure of the central tendency of the distribution. For the given scenario with alpha = 7 and beta = 12, the mean is calculated as alpha / (alpha + beta). Substituting the values, we find that the mean equals 7 / (7 + 12) = 7 / 19, which is approximately 0.3684.

This implies that, on average, erroneous tax returns tend to fall at about 36.84% into the distribution. A higher mean indicates a shift toward the higher end of the distribution, providing insights into the typical behavior of the variable represented by the beta distribution in this context.