Skip to content
We use only essential cookies to keep you signed in and remember your preferences. See our Cookie Policy.
TestStop
MocksPracticeResourcesIndiaBlogPricing
Sign in
Questions › DSE › DSE 2021 › Q41
4 marks, −1Statistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsModerateabout 2 min

DSE 2021 Question 41: Random variables and standard distributions

Suppose XXX is a random variable which takes values in the interval [−12,12][-\tfrac{1}{2}, \tfrac{1}{2}][−21​,21​]. The probability distribution function is denoted by Φ(x)\Phi(x)Φ(x). Which of the following is certainly true?

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Suppose X is a random variable which takes values in the interval [-1/2, 1/2]. The probability distribution function is denoted by Φ(x). Which of the following is certainly true? (A) For any real numbers a, b with b > a, Φ(b) > Φ(a) (B) For any real numbers a, b in the interval [-1/2, 1/2] with b > a, Φ(b) > Φ(a) (C) Expectation of X equals 0 (D) Variance of X cannot exceed 1

Also written as: Suppose X is a random variable which takes values in the interval [-1/2, 1/2]. The probability distribution function is denoted by Phi(x). Which of the following is certainly true?

Random variables and standard distributions has come up 173 times in 7 exams since 2005.

What this question tests

This question is on Random variables, PMFs, PDFs and CDFs, part of Random variables and standard distributions in Statistics.

Describing a random variable by its mass, density or distribution function.

TestStop has 33 past-paper questions on this subtopic.

Practise Random variables and standard distributionsMore on Random variables, PMFs, PDFs and CDFs

Similar questions from other papers

  • CUET-PG 2026 · Q35Given below are two statements: Assertion A: A random variable is a numerical description of the outcome of an experiment. Reason R: The particular numerical value of a…
  • GATE 2026 · Q41Suppose, a random variable X follows a Poisson distribution with parameter λ=25. The coefficient of variation of the distribution is (rounded off to two decimal places)
  • IIT JAM 2026 · Q42It is given that Prob(-1≤ z≤ 1)=0.683, Prob(-2≤ z≤ 2)=0.954, and Prob(-3≤ z≤ 3)=0.997, when z follows a standard normal distribution. If X follows a normal distribution…
  • CUET-PG 2025 · Q20Suppose that the random variable X takes on the values: -1, 0, and 2 with probability 1/8, 1/2 and 3/8. Find the expected value of X.
  • GATE 2025 · Q41If X is a continuous random variable whose probability density function is given by f_X(x) = { 1/x² for 1 < x < ∞; 0 elsewhere } Then the median of X is (in integer)

Question from the DSE 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.