self-study

  1. How do I calculate the standard error of the $\chi^2$ statistic?

  2. Estimating the randomness of a LCG
  3. Difference between contextual anomaly and collective anomaly

  4. Proof: Unbiased Correlation Estimator

  5. What is meant by "let $X_2$ and $v$ be the residuals obtained from regressing $X_3$ on $X_1$"?
  6. What is the difference between period cycle and seasonality?

  7. In PCA, do we have to center and normalize eigenvectors or solely to normalize them?

  8. Sufficient Statistics for Hierarchical Model
  9. Expected value of a marginal distribution when the joint distribution is given

  10. Markov Chain - "Expected Time"
  11. Showing that estimator is consistent

  12. Indicator Random Variable

  13. Kendall correlation between $X$ and $X^2$

  14. A box has an unknown number of tickets..Estimation
  15. An 'easy' exercise on conditional expectations and filtrations

  16. Computing the posterior mean using a Gaussian prior?

  17. Difference between complete and incomplete designs (DOE)

  18. How to show order statistic is sufficient
  19. Confidence interval based on MLE

  20. Beginner level -- applying machine learning to predict unknown pattern

  21. How to prove probability problem
  22. Joint Probability Table and Dependent/Independent Probabilities
  23. If $X$ and $Y$ are independent Normal variables each with mean zero, then $\frac{XY}{\sqrt{X^2+Y^2}}$ is also a Normal variable
  24. Maximum likelihood and sufficient statistics

  25. What is the derivative of the ReLU activation function?
  26. How to determine if sample with standard deviation is normally distributed?

  27. Hiding a Regression Model from Professor (Regression Battleship)
  28. Fisher's Information for Laplace distribution

  29. Finding the expected value for this uniform
  30. Calculating Joint Probability from Conditional Probability
  31. How to simplify summation?

  32. how to get 2/15 as the probability?
  33. Has this expectation been computed correctly?
  34. How to calculate conditional variance?

  35. Marginal densities from joint of beta and gamma

  36. effect of population mean on type 1 error rate
  37. How is the error term related to the dependent variable in a regression model?

  38. Kaplan-Meier Estimate with no censoring

  39. Why is there a "2" when deriving the OLS estimator in vector notation?

  40. Confidence-Interval - Proof the Upper and Lower limit
  41. Define the joint pmf of a particle moving randomly on a grid

  42. Confidence/credibility intervals for a bernoulli trial
  43. Geometric interpretation of W and b in SVM
  44. Least squares estimator in a time series $\{Y_t\}$

  45. Limiting distribution of random variables with different distributions

  46. How to find a random variable that has a given distribution?

  47. If higher order moment is finite, then lower order moment finite?
  48. Distribution of extreme values, case of uniform

  49. probability of a function of poisson random variable

  50. Is $y_t=\beta_0+\beta_1t+z_t$ stationary?
  51. MLE uniform distribution with varying supports
  52. Statistic T-Test & T-table

  53. Gelman & Hill ARM textbook, Question 3.2, R-squared

  54. Find the probability that in a group of 23 people, exactly 3 people have birthdays on the same day

  55. An example: LASSO regression using glmnet for binary outcome

  56. Calculate for the standard error

  57. Order statistic, probability
  58. Finding Bellman equations for a specific policy
  59. Alternative to The Elements of Statistical Learning: Data Mining, Inference, and Prediction
  60. Meaning of "baseline age" in a medical study

  61. Given E(x) check if u is an unbiased estimator
  62. If we consider a model of stock price where the prices at time $t=1,2$ are $S(t,\omega)=S(0)(\frac{1}{2}+t\omega), \omega\in\Omega=[0,1]$
  63. Effects of different changes on test statistic

  64. MME for exponential family

  65. how to prove SST follows a chi-square distribution with (m−1) degrees of freedom

  66. Proof of variance of stationary time series

  67. Questions about confidence intervals

  68. Playing hands from limited sized decks
  69. Identity relating Bayes risk to bias
  70. Determining an MLE
  71. Moment Generating Function - Negative Binomial

  72. Find mean and variance of random variable using moment generating function

  73. How to prove three properties of the moment generating function?

  74. CDF of Z=XY with X~Uniform(0.5,1.5) and Y~Uniform(0.8,1.5)

  75. Question about unbiased estimate for $P(X<a)$

  76. Question regarding derivation of variance for AR(1) when rho is less than 1
  77. Showing sufficiency using the Fisher-Neyman factorization theorem
  78. Mean and variance of a vector $W = (X', Y')'$

  79. Help understanding Linear Model in ESL book

  80. MLE for variance of a lognormal distribution
  81. Misinterpretation of statistics: falsely accused
  82. Calculate probability using tree diagram and bayes theorem
  83. Is it normal for the Kolmogorv-Smirnov p value to fluctuate when using randomly generated data?

  84. good lightweight conceptual/mathematical introduction to Bayesian statistics?

  85. Detecting Change in Usage Patterns of an Application

  86. How can I compute the lower and upper bounds of a confidence interval in a linear regression problem?

  87. How to know if a data follows a Poisson Distribution in R?
  88. Moment generating functions of continous random variables at 0

  89. How do you calculate the mean and variance of a random var with a distribution function that has a parameter with its own distribution function?

  90. Basu's Theorem Proof
  91. For Multivariate Gaussian Mixture Models, What will happen if all mixing probabilities are equal?

  92. Voting between classifiers : How to prove it works?
  93. Calculate market share based on probability
  94. How can I calculate t-score without knowing true population mean?
  95. Why does MAP converge to MLE?

  96. CRBD design question about difference of means

  97. K-means algorithm to K-lines algorithm

  98. Zero-mean RV $X$, probability of being positive using moments

  99. Model selection and estimation for pseudo out-of-sample forecasting
  100. draw roc curve on an example of 10 probability scores