Final answer:
The mean of a continuous uniform distribution over the interval [-2, 1] is -0.5, calculated using the formula for the mean of uniform distributions.
Step-by-step explanation:
The mean of X, which has a continuous uniform distribution over the interval [-2, 1], is -0.5.To calculate the mean of a continuous uniform distribution, we use the formula μ = (a + b) / 2, where 'a' and 'b' are the lower and upper bounds of the interval respectively. Since X ~ U(-2, 1), we plug in the values to get μ = (-2 + 1) / 2, which simplifies to μ = -0.5. This outcome is expected since, in a uniform distribution, the mean is simply the midpoint of the interval over which the variable is uniformly distributed.
Additionally, a uniform distribution assumes that all values within its range are equally likely to occur, hence the mean is centrally placed within the range.The mean of a continuous uniform distribution over the interval [a, b] is given by the formula:Mean (µ) = (a+b)/2In this case, the interval is [-2, 1], so the mean of X is:Mean (X) = (-2 + 1)/2 = -0.5