Let X be a continuous random variable with a probability density function given by f(x) = ax for 0 ≤ x < 1; f(x) = a for 1 ≤ x < 2; f(x) = -ax + 3a for 2 ≤ x < 3; and f(x) = 0 for x ≥ 3. The value of 'a' 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.