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 › GATE › GATE 2024 › Q41
1 markStatistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsModerateabout 2 min

GATE 2024 Question 41: Random variables and standard distributions

For the following function f(x)f(x)f(x) to be a probability density function, the value of ccc will be ______ (rounded off to two decimal places).

f(x)={cx0<x<4 and c>00otherwisef(x) = \begin{cases} \dfrac{c}{\sqrt x} & 0<x<4 \text{ and } c>0 \\ 0 & \text{otherwise} \end{cases}f(x)=⎩⎨⎧​x​c​0​0<x<4 and c>0otherwise​

Answer and worked solution

Checking your account…

Plain-text version

For the following function f(x) to be a probability density function, the value of c will be (rounded off to two decimal places). f(x) = { c/√x 0<x<4 and c>0; 0 otherwise }

Also written as: For the following function f(x) to be a probability density function, the value of c will be (rounded off to two decimal places). f(x) = { c/sqrt(x) 0<x<4 and c>0; 0 otherwise }

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.

Take this paper as a timed mockMore 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 GATE 2024 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.