Question

A continuous random variable x is uniformly distributed over the interval [12, 18]. What is the variance of x − 15?

Answer 1

If the variable is normally distributed over the interval [12,18] then the variance of x is 3.

Given that the variable is normally distributed over the interval [12,18].

We are required to find the variance of x if x is normally distributed over the interval [12,18].

Variance is a statistical measure which determines the dispersion of values in a population. Variance is basically the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is  measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value.

Variance when interval [a,b] is given as under:

Variance =$(b-a)^{2}/12$

=$(18-12)^{2} /12$

=$(6)^{2}/ 12$

=36/12

=3

Hence the variance of x is 3 if x is distributed normally over the interval [12,18].

Learn more about variance at brainly.com/question/9304306

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