{"blocks": [{"key": "46e698ee", "text": "Scenario", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "1d8e14be", "text": "Interview assessing fundamental statistics knowledge for a data-science role", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "1fcb0f85", "text": "Question", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "36b0fc76", "text": "Given an i.i.d. sample from a Normal distribution, derive the maximum-likelihood estimators for its mean and variance. 2) For random variables X and Y with a known joint pdf, derive the conditional distribution of X given Y. 3) Write the pdf and cdf of the standard Normal distribution. 4) Starting from a concrete estimation task, list and justify the assumptions required for the estimator to be unbiased.", "type": "unordered-list-item", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "5b8269f0", "text": "Hints", "type": "header-two", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}, {"key": "3cc1d0be", "text": "Use log-likelihood differentiation, f(x|y)=f(x,y)/f_Y(y), Φ(z)=∫_{-∞}^z φ(t)dt, and recall iid sampling and finite expectation conditions for unbiasedness.", "type": "unstyled", "depth": 0, "inlineStyleRanges": [], "entityRanges": [], "data": {}}], "entityMap": {}}