Expectation & Variance of a r.v Y with Geometric-like Distribution| UPSC ISS 2024 Paper-1 Problem-35 скачать в хорошем качестве

Expectation & Variance of a r.v Y with Geometric-like Distribution| UPSC ISS 2024 Paper-1 Problem-35

This explanation calculates the expectation and variance of a random variable \(Y\) whose PMF is weighted by powers of \(2\). Using sums of arithmetic-geometric progressions (AGP), the expectation of \(Y\) is found to be: \[ E[Y] = 1, \] and the second moment: \[ E[Y^2] = 3. \] Thus, the variance is: \[ \text{Var}(Y) = E[Y^2] - (E[Y])^2 = 3 - 1 = 2. \] Although \(Y\) resembles a geometric distribution, its variance is 2, not 1. This detailed walkthrough showcases how to handle sums involving AGPs for moments calculation in probability. #upsc #upscmotivation #upscaspirants #upscpreparation #civilservices #civilservicesexam #upscexam #upscstudy #upscstudents #ias #ips #ifs #studywithme #statisticsexplained #hypothesistesting #statistics #learningmadeeasy #education #ytshorts #maths #conceptclarity #indianstatisticalservice #statisticalmethods #ritwikmath #probability #statisticsoptional #expectation #variance #arithmeticgeometricprogression