self-study

  1. How to bound a probability with Chernoff's inequality?

  2. May I use t-test for hypothesis, if my sample's n=22, s=1000, and population's s=1600(n=60)? Or it doesn't make sense?

  3. proving consistency for a sequence of Bernoulli random variables

  4. Show that Sufficient statistic is complete

  5. Find marginal distribution of $K$-variate Dirichlet

  6. Showing $\frac{2X}{1-X^2}$ is standard Cauchy when $X$ is standard Cauchy

  7. A problem on estimability of parameters

  8. Can I use z test for a sample that have no outliers?
  9. Proof for sum of squares formula
  10. Is there a Bayesian decision rule based on likelihood alone? And if so, what is its error rate?
  11. Consistency of a sequence of Bernoullis
  12. UMVUE explanations
  13. Does Akaike's Information Criterion correspond to a type of regularization?
  14. Model selection and estimation for pseudo out-of-sample forecasting

  15. Feature scaling and mean normalization
  16. Expected number of tries required for consecutive successes
  17. How to intuitively explain the maths behind overdispersion?

  18. Accuracy measures in training/test split of time series
  19. Using Central Limit Theorem to Prove Claims About Distributions? (Desperate)
  20. Finding the distribution of $2\theta X_i^2$

  21. Help in convolution operation
  22. Why does the p-value for z=x correspond to the negative x in a z-score table?

  23. Specification of logical node (with distribution?) in WINBUGS

  24. How do I find the mean of a difference?

  25. Find the posterior density of theta, given prior with exponential density and samples from normal distribution

  26. Is this hypothesis test correct?
  27. Kernel exercise
  28. Linear models and hypothesis testing
  29. Basketball free throw probability
  30. MSE and MLE with Poisson distribution

  31. How much statisticians use numerical analysis while comparing critical values?

  32. the graph of log(-log) for Cox model on survival analysis
  33. frequency distribution table for a question

  34. Expectation maximization when support of likelihood is parameterized

  35. Difference between complete and incomplete designs (DOE)

  36. Gaussian process regression understanding
  37. the mean median and standard deviation are respectively

  38. Simulation: variance of sampling dist. of means or of dataset itself?
  39. If a node Z in a conditional probability query P(X|capY) is not requisite, how do we know that there exist networks where P(X|Y) are not equal?
  40. surrogate end point

  41. Proving that overspecifying a linear model increases variance

  42. likelihood ratio test for Geometric distribution

  43. Finding the biases and standard errors of a Cauchy distribution using R

  44. Expected value the device corrupts

  45. Expected value of absolute difference of random variables
  46. How to compute transition probability matrix by using the cohort estimator in the Markov case and non-Markov case

  47. Usefulness of integral operator as generalization of a matrix? (Intuition)

  48. Is there a closed form solution to the expected value of the maximum of iid random variables?

  49. Standard error of the sampling distribution and standard deviation

  50. PCA and diagonalization of the covariance matrix
  51. Proving that MLE is max(x1,...,xn)
  52. Calculating a probability for an individual not selected

  53. How to add and multiply distributions?

  54. regression vs correlation: the motivation for using each
  55. An 'easy' exercise on conditional expectations and filtrations

  56. Importance sampling - derivation
  57. solve a differential equation

  58. Maximum likelihood for data from a Binomial distribution
  59. Proportion of correct guesses knowing the true probabilities

  60. Covariance Matrices

  61. Cochran's rules for contingency table

  62. Showing that H(X|Z)= H(Y) for Z=X+Y, with X,Y independent
  63. Moment generating function of the natural sufficient statistics of Gamma distribution

  64. $E[e^{cX}]$ where $c < 0$ and $X$ is lognormally distributed
  65. How to find the levels (+ or -) using the words in a Fractional Factorial?
  66. Bias term dimension in XOR learning

  67. Evaluating decision tree

  68. Expected value of a marginal distribution when the joint distribution is given

  69. In PCA, do we have to center and normalize eigenvectors or solely to normalize them?
  70. MOOC based on Statistical Inference by Casella and Berger?

  71. Gelman & Hill ARM textbook, Question 3.2, R-squared
  72. Outlier detection and normality assumption
  73. Help understanding a paragraph in Kadane's book Principles of uncertainty

  74. Assign the design points to 2^2 design in 6 blocks of size 2?

  75. If X and Y are perfectly correlated, what is the correlation of X+Y and X-Y?

  76. How can I justify using higher number of lags in Ljung-Box test?

  77. How to identify if parameters are estimable, after defining a design matrix
  78. how to prove SST follows a chi-square distribution with (m−1) degrees of freedom

  79. Matrix of regression coefficients
  80. Possible to use moment generating function of standard normal to find variance of noncentral $\chi^{2}$?

  81. What is the empirical frequency?

  82. How does one account for Did-Not-Complete data in temporal averages?

  83. Breusch-Godfrey for time series model residuals

  84. Why is the Fisher information the inverse of the (asymptotic) covariance, and vice versa?

  85. Question about Spectral Clustering equation in ESL

  86. Markov Chain depending on a value

  87. Examples where the evaluation of the posterior distribution $p(Z|X)$ of the latent variables $Z$ is a central task?

  88. Significance of coefficient from two different regressions
  89. Prove that $E[g(X)] = \int_{-\infty}^{\infty}G(t)\phi(t) dt$
  90. What is the expected number of occurrences of a 9-mer in 500 random DNA strings, each of length 1000?

  91. Characteristic function of distribution
  92. Characteristic Function proof

  93. How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots , x_n$?

  94. Prove $A(A+B)^{-1}B=B(A+B)^{-1}A$
  95. textbooks/literature/resources for online learning/ time series/ sequential analysis?
  96. T-test formula when population standard deviation is known

  97. What is cov(X,Y), where X=min(U,V) and Y=max(U,V) for independent uniform(0,1) variables U and V?
  98. Why a linear regression cannot obtain a zero classification error on a predictor that perfectly classifies the target?

  99. How to Get SST when only given the Means of the Treatment Groups?

  100. What's higher, $E(X^2)^3$ or $E(X^3)^2$