Let a continuous random variable X have the probability density function (pdf) given by f(x) = 3x2θ3 for 0 ≤ x ≤ θ (where θ > 0), and f(x) = 0 otherwise. The mode of X is:

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.