If f(x) = 3(1 - 2x2) for 0 < x < 1 and f(x) = 0 otherwise, is a valid probability density function of X, then find the value of the probability P(14 < x < 13).

The mean and standard deviation of a Binomial distribution with parameters n, p, and q (where q = 1 - p) are respectively:

In a Binomial Distribution, the formula for calculating the standard deviation is:

Given below are two statements: Statement I: The F-distribution is defined as the ratio of two independent chi-square random variables, each divided by its respective degrees of freedom. Statement II: The Student's t-distribution is symmetric about the origin (mean = 0) with a bell shape similar to the standard normal distribution.