Question

In certain experiments, the error made in determining the solubility of a substance is a random variable having the uniform density with a= -0.025 and B=0.025. What are the probabilities that such and error will occur over the interval from -0.04 to 0.04?

Answer 1

The probability of an error occurring over the interval from -0.04 to 0.04 in solubility determination, when errors are uniformly distributed between -0.025 and 0.025, is zero as the interval does not overlap with the defined range of the random variable.

Step-by-step explanation:

Probability of an Error in Solubility Determination

In the experiment described, the error made in determining the solubility of a substance is a random variable with a uniform distribution between a = -0.025 and B = 0.025.

For uniform distributions, the probability of an event occurring within a certain interval is proportional to the length of that interval. Since the total span of the distribution is 0.025 - (-0.025) = 0.05, and the interval of interest, from -0.04 to 0.04, falls entirely outside the defined range of the random variable, the probability of such an error occurring over this specific interval is zero.

This is because no part of the interval from -0.04 to 0.04 overlaps with the defined range of our uniform random variable, hence no probability mass lies within this range.