UPCET / UPSEE Random Variables — practice questions

Explore 2 free Random Variables questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Random Variables with Quill →

Random Variables questions and exercises with answers

Showing questions 1–2 of 2.

A **random variable** is best defined as:Read the answer and worked solution →When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:Read the answer and worked solution →

Worked practice questions

A random variable is best defined as:

The probability of an event
A real number chosen by random guess
A real-valued function defined on the sample space of a random experiment
A variable with arbitrary letter name

Show answer and solution

Correct answer: C. A real-valued function defined on the sample space of a random experiment

**A random variable X is a function X :** S → ℝ from the sample space to real numbers. It assigns a numerical value to every outcome of the random experiment. Conventionally denoted by capital letters (X, Y, Z).

Open this question →

When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:

$\{2, 3, ..., 12\}$
$\{1, 2, ..., 12\}$
$\{0, 1, ..., 12\}$
$\{1, 2, ..., 36\}$

Show answer and solution

Correct answer: A. $\{2, 3, ..., 12\}$

Each die shows 1 to 6. Minimum sum 1+1 = 2, maximum sum 6+6 = 12. So range = {2, 3, 4, …, 12}. (11 distinct values out of 36 outcomes.)