List of top Statistics Questions

Let \( \{a_n\} \) be a sequence defined as follows:
\[ a_1 = 1 \quad \text{and} \quad a_{n+1} = \frac{7a_n + 11}{21}, \quad n \in \mathbb{N}. \] Which of the following statements is TRUE?

A bag contains 3 red, 4 white and 5 blue balls. If two balls are drawn at random, then the probability that they are of different colours is:

There are 5 positive numbers and 6 negative numbers. Three numbers are chosen at random and multiplied. The probability that the product is a negative number is:

Two fair dice are rolled. Then the probability of getting a composite number as the sum of face values is equal to:

If $f(x) = \begin{cases} 3(1 - 2x^2), & 0<x<1 \\ 0, & \text{otherwise} \end{cases}$ is a probability density function of $X$, then $P\left(\frac{1}{4}<x<\frac{1}{3}\right)$ is