PDF of Y = X² ; E[Y] & Var(Y) | UPSC IFoS 2025 Statistics Paper 1 | Problem-2(a) | RitwikMath скачать в хорошем качестве

PDF of Y = X² ; E[Y] & Var(Y) | UPSC IFoS 2025 Statistics Paper 1 | Problem-2(a) | RitwikMath

Solve *Question 2 Part 1* from **UPSC Indian Forest Service 2025 Statistics Optional Paper 1**! For continuous RV X with PDF \( f_X(x) = \frac{x+1}{2}, -1 \leq x \leq 1 \), and \( Y = X^2 \): Derive PDF of Y using **transformation method**: \( f_Y(y) = \frac{1}{2\sqrt{y}}, 0 y 1 \) (verified as valid PDF). Compute *E[Y] = \(\frac{1}{3}\)* and *Var(Y) = \(\frac{4}{45}\)* using both Y's PDF and original X moments. Master *PDF transformations* and *moment calculations* for UPSC Statistics! #UPSC #UPSCIFS #IndianForestService #UPSCStatisticsOptional #UPSC2025 #PDFTransformation #TransformationOfVariables #ExpectationVariance #ContinuousRandomVariable #StatisticsForUPSC #IndianStatisticalService #UPSCPreparation #ProbabilityTheory #ForestServiceExam #UPSCOptionalStatistics #UPSCForestService #ExamPreparation #CompetitiveExams