Question:
Let X be a continuous random variable defined on [0,1] such that its probability density function f(x) = 1 for 0 ≤ x ≤ 1 and 0 otherwise. Let Y = loge (X + 1). Then the expected value of Y is ____. (rounded off to 2 decimal places)
Let X be a continuous random variable defined on [0,1] such that its probability density function f(x) = 1 for 0 ≤ x ≤ 1 and 0 otherwise. Let Y = loge (X + 1). Then the expected value of Y is ____. (rounded off to 2 decimal places)
Updated On: Jan 24, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 0.38
Solution and Explanation
The correct answer is:0.38 to 0.39
Was this answer helpful?
2
2
Top Questions on Conditional probability
- Let the probability density function of a random variable \( x \) be given as \[ f(x) = ae^{-2|x|} \] The value of ‘a’ is ________.
- GATE EE - 2022
- Engineering Mathematics
- Conditional probability
Let \( X \) and \( Y \) be continuous random variables with the joint probability density function
Then \( E(X | Y = -1) \) equals}
- IIT JAM MS - 2017
- Statistics
- Conditional probability
- Let \( E \) and \( F \) be two events with \( 0<P(E)<1 \), \( 0<P(F)<1 \) and \( P(E) + P(F) \geq 1 \). Which of the following statements is (are) TRUE?
- IIT JAM MS - 2017
- Statistics
- Conditional probability
Questions Asked in GATE Metallurgy exam
- At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate w=7rad/s. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is _____rad/s (rounded off to 2 decimal places).
- GATE Metallurgy - 2024
- Principles of the design of machine elements such as bolted, riveted and welded joints
- In an arc welding process, the voltage and current are 30V and 200A, respectively. The cross-sectional area of the joint is 20 mm2 and the welding speed is 5mm/s. The heat required to melt the material is 20 J/s. The percentage of heat lost to the surrounding during the welding process is ____(rounded off to 2 decimal places).
- GATE Metallurgy - 2024
- Principles of welding, brazing, soldering and adhesive bonding
- Let f(z) be an analytic function, where z = x + iy. If the real part of f(z) is cosh x cos y, and the imaginary part of f(z) is zero for y = 0, then f(z) is
- GATE Metallurgy - 2024
- Analytic functions
- Steady, compressible flow of air takes place through an adiabatic converging- diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If E and F denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?
- GATE Metallurgy - 2024
- Basics of compressible fluid flow
- A set of jobs U, V, W, X, Y, Z arrive at time t = 0 to a production line consisting of two workstations in series. Each job must be processed by both workstations in sequence (i.e., the first followed by the second). The process times (in minutes) for each job on each workstation in the production line are given below.
Job U V W X Y Z Workstation 1 5 7 3 4 6 8 Workstation 2 4 6 6 8 5 7
The sequence in which the jobs must be processed by the production line if the total makespan of production is to be minimized is- GATE Metallurgy - 2024
- Principles of non-traditional machining processes
View More Questions