Content Specialist

How to estimate the total number of Nazi Tanks?

**Historical Context** During World War II, Allied intelligence faced the challenge of estimating German tank production. This led to the development of statistical methods that significantly outperformed traditional intelligence gathering. Here's how the simulation works: 1. We have a secret number of tanks (500 in this case). 2. We pretend to "capture" 5 tanks and look at their serial numbers. 3. Based on these 5 numbers, we try to guess the total number of tanks. 4. We repeat this process 1000 times to see how good our guessing methods are. Here's the strategy: - The "Simple" method (MLE): We just use the highest number we see. - The "Smart" method (Unbiased): We use a slightly more complicated calculation that tries to account for the tanks we didn't see. Observations: 1. The "Simple" method (blue) tends to guess too low. Its average guess is about 416 tanks, which is less than the real 500. 2. The "Smart" method (orange) does better. Its average guess is about 498 tanks, very close to the real 500! 3. But notice how the orange bars are more spread out. This means the "Smart" method can sometimes be way off, even though it's better on average. 4. The "Simple" method is more consistent (the blue bars are more bunched together), but it's consistently too low. **Estimation Methodology** **1. Basic Maximum Likelihood Estimator** The simplest approach uses the maximum observed serial number (m) as an estimator: N̂ = m While simple, this estimator is biased low, as P(N̂ ≤ N) = 1. **Improved Estimators** **Sample Maximum Plus Average Gap** A more sophisticated estimator adds the average gap between observed serial numbers: N̂ = m + (m - k) / k Where: - m: maximum observed serial number - k: number of observed samples This can be interpreted as the maximum plus the average gap, providing a less biased estimate. **Derivation from Order Statistics** The estimator can be derived from order statistics. For a sample of size k from a uniform discrete distribution on {1, ..., N}: E[m] = N * k / (k + 1) Solving for N yields the unbiased estimator: N̂ = m * (k + 1) / k - 1 **Probability Analysis** The probability of observing a specific set of serial numbers {s₁, ..., sₖ} given N tanks is: P({s₁, ..., sₖ} | N) = k! / (N * (N-1) * ... * (N-k+1)) Maximizing this probability (or its logarithm) with respect to N yields the maximum likelihood estimator.

300+ Companies paying 12LPA+ base for SDE-1 role in India

Acko Adobe Airbase Airbnb Airbus Airtel X Labs Ajio Akamai AlphaGrep Alphonso Amagi Amazon American Express Angel One Ansys Anthem Apna AppDynamics Arcesium Arista Atlassian AutoDesk Auzmor Avail Finance Avalara BCG BNY Mellon Bain & Company Bankbazaar Belzabar Bharatpe Bigbasket Biofourmis Bizongo Blackbuck Blinkit BloomReach Booking Bright Money Broadcom Browserstack Bukuwarung Buyhatke Byjus C2FO Cadence CashFree Chargebee Chegg Chronus Software Cisco Citi Bank Citrix Citymall Clarisights ClearQuote ClearTax ClearTrip Cloootrack Cloud Lending Clumio Credgenics Codenation Cogoport Cohesity Coinbase Coinswitch CommerceIQ Commvault Confluent CouchBase Cred Credit Suisse Crowdfire Cult Fit DE Shaw Daily Rounds Datadog Dealshare Delhivery Dialpad Directi Dp world Dream 11 Dremio Druva Duetshe bank Dunzo Eightfold ai Electronics Arts Eltropy Endurance Enfusion Epifi Expedia Falabella Fanclash Far Eye FarEye Fedility Investments Fleetx Flipkart Flock Fraazo FreeCharge FreshMenu FreshWorks FrontRow FunPlus GE Health Care Games 24x7 GamesKraft Gartner Glance Gojek Goldman sachs GoodWorker Google Grab Graviton Groupon Groww Gupshup Harness Headout Hedge Fund Hotstar Idrive Indeed IndiaMart Indiagold Indmoney InfoEdge Informatica Infoworks Inmobi Innovacer InsideView Instabase Intel Intuit Ion Trading Itilite Ixigo Jio JPMC Jumio Jungle Games Juniper Networks Jupiter Money Juspay KLA Khatabook Komprise Kuvera LambdaTest Leap Finance Leena ai Lenskart Licious Limeroad Linkedin Linq Livspace Loco MPL Magnitude MakeMyTrip Mastercard MathWorks McKinsey Medianet Meesho Meidatek Mentor Graphics Mfine Microsoft MindTickle MoenGage Money Control Moneyview MoonFrog Morgan Stanley MotorQ MSC MyKaarma Myntra NK Securities Nas Academy National Instruments Navi Nektar ai NetApp Netomi NewFold Digital Nference Nike Ninjacart NoBroker Noccarc Nurture Farm Nutanix Nvidia OCI OLX Group OkCredit Ola Oppo Oracle Oyo Palo Alto PayU Paypal Paytm Peak Ai PharmEasy Philips Phonepe Pickrr Plivo Pl

I have received offers from Databricks and NK securities as new grad. Which is better considering future career prospects?