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 2020 › Q5
4 marks, −1Statistics › Random variables and standard distributions › Transformations and order statisticsModerateabout 3 min

DSE 2020 Question 5: Random variables and standard distributions

YYY is uniformly distributed on [0,2][0,2][0,2]. For X=eYX=e^{Y}X=eY, the value of the cumulative distribution function of XXX at x∈[1,e2]x\in[1,e^{2}]x∈[1,e2] is

Tap an option to check your answer.

Answer and worked solution

Checking your account…

Plain-text version

Y is uniformly distributed on [0,2]. For X=e^Y, the value of the cumulative distribution function of X at x∈[1,e²] is (A) 2⁻¹ln x (B) 4⁻¹ln x - 2⁻¹ (C) ln x (D) ln x - 1

Also written as: Y is uniformly distributed on [0,2]. For X=e^Y, the value of the cumulative distribution function of X at x in [1,e^2] is

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

What this question tests

This question is on Transformations and order statistics, part of Random variables and standard distributions in Statistics.

The distribution of a function of a random variable, and of the largest or smallest of several.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q23X and Y are independent with F_X(x) = 1 - (3/4)^x and G_Y(y) = 1 - (2/3)^y for x, y = 1, 2, 3, …. Let Z =…
Practise Random variables and standard distributionsMore on Transformations and order statistics

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 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.