Uniform DistributionWhat is the probability of the random variable X lying between -1.5 and +2.5, i.e. P(-1.5<X<2.5)?

To calculate the probability of a random variable X lying between -1.5 and 2.5 in a uniform distribution, we need to know the parameters of the distribution, namely the lower limit (a) and the upper limit (b).

The probability density function of a uniform distribution is 1/(b-a) for a ≤ x ≤ b and 0 otherwise.

The probability that X lies between -1.5 and 2.5 is given by the integral from -1.5 to 2.5 of the probability density function.

If we assume that the distribution is uniform between -1.5 and 2.5, then the probability is 1, because the entire distribution lies within this range.

If the distribution is uniform on a larger range, then the probability would be less than 1. For example, if the distribution is uniform between -2 and 3, then the probability would be the length of the interval (-1.5 to 2.5) divided by the length of the entire range (-2 to 3), which is 4/5 = 0.8.

If the distribution is uniform on a smaller range entirely within -1.5 to 2.5, then the probability would be 1, because any value that X can take is within this range.

If the distribution is uniform on a range that partially overlaps with -1.5 to 2.5, then the probability would be the length of the overlapping interval divided by the length of the entire range.

Without knowing the exact parameters of the distribution, we cannot calculate the exact probability.