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Questions › GATE › GATE 2025 › Q44
2 marksStatistics › Random variables and standard distributions › Random variables, PMFs, PDFs and CDFsEasyabout 1 min

GATE 2025 Question 44: Random variables and standard distributions

If XXX is a continuous random variable whose probability density function is given by

fX(x)={cx3+0.25for 0≤x≤1,c∈R0elsewheref_X(x) = \begin{cases} cx^3 + 0.25 & \text{for } 0 \le x \le 1, c \in \mathbb{R} \\ 0 & \text{elsewhere} \end{cases}fX​(x)={cx3+0.250​for 0≤x≤1,c∈Relsewhere​

Then the value of ccc is ______ (in integer)

Answer and worked solution

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Plain-text version

If X is a continuous random variable whose probability density function is given by f_X(x) = { cx³ + 0.25 for 0 ≤ x ≤ 1, c ∈ ℝ; 0 elsewhere } Then the value of c is (in integer)

Also written as: If X is a continuous random variable whose probability density function is given by f_X(x) = { cx^3 + 0.25 for 0 <= x <= 1, c in R; 0 elsewhere } Then the value of c is (in integer)

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.

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Question from the GATE 2025 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.