# self-study

1. ### What is the smallest value of r that gives a test of size not exceeding 0.05?

0down votefavorite I've been given a question that I don't understand. Question: Consider a test which rejects H0 if the number of observed successes is ≥r≥r , where r is some number. What is the smallest value of r that gives a test of size not exceeding 0.05? We have been given: o=50 ,for...
2. ### CDF of a PDF with a negative power

I need to solve the following problem: For a marine hull insurance policy, a claim occurs with probability 0.DD, where DD represents the two date-digits of your birthday (DD.MM.YYYY). If a claim occurs, it has a probability density given by fB(x)=c·x^(−1.5), 1<x<YYYY, where YYYY are the...
3. ### Distribution of X+Y of a bivariate normally distributed (X,Y)

I need to give the distribution of $X+Y$ and $X-Y$ knowing that $(X,Y)$ is bivariate normally distributed with marginal means 1, marginal variances 1 and correlation $p=2$.Is it right that the marginal mean are simply $E(X)=1$ and $E(Y)=1$ ?I don't see where I should start knowing that.
4. ### Computer game log normally distributed

I'm playing a computer game and I want to boost the high score. I assume that attempts are independent (say, you do not improve by playing), and in each game my achieved points are lognormally distributed with mean 500 and variance 1’000’000. How often do I have to play so that your high score...
5. ### Sudokua problem using related binomial distribution

It is given: If you succeed to solve a Sudoku with probability 0.4 and you try many times, how likely is it that you succeed twice before you fail 5 times? What is the expected number of failures before two successes? I don't understand which one between the binomial, geometric, negative...
6. ### Resulting expected value of a bounded exponential pdf

I need to determine the distribution function of an exponential random variable with mean 2, given that its outcome is larger than 2 and give the resulting expected value? I know that the mean is 1/lambda, so lambda should be 1/2. I get that way 0.5*e^(-0.5x) >= 2. How can I deal with the...
7. ### Distribution function of an exponential random variable

Let Y ⇠ Exp(2) be the size of an insurance loss. If the insurance company pays min(Y, 4), what is the variance of that payment? I know that lambda =2 If I put that in the pdf I get: 2*e^(-2x). I don't understand how to use the information given by min(Y, 4)
8. ### Definition of random variable with respect to event space

It is given that: We toss two dice with sample space Ω = {(i, j), 1 ≤ i, j ≤ 6} and the σ-algebra is generated by the events Ak = {(i,j) : max(i,j) = k} (k = 1, . . . , 6). Show that whereas X1(i, j) = max(i, j) is a random variable in the corresponding probability space, X2(i, j) = i + j is...
9. ### Prove: Birth-death chain has stationary distribution -> satisfy detail bal. equations

I'm working my way through a course in stochastic processes but came across this Lemma in my coursebook where they didn't show the working (Lemma 8.5). I'm not familiar with doing proofs and it isn't taught in any of my courses but I can read/understand them, how did they reach the conclusion of...
10. ### Calculating Overall Relative Bias

I am in some trouble to understand how is to calculate the overall relative bias. In this link, there are results of overall relative bias in "Parameter estimates" sub-section under "Results" section. There they mentioned that : Could you please explain me how did they calculate it? I had...
11. ### Project Issue.

I am a student of statistics discipline. I have to conduct a project which i can apply in society or nation. My preferable topics are agricultural/technological/environmental statistics. But i am not understanding how can i specialize my topic, make it applicable and can have an ample online...
12. ### Obtaining sample variance from grouped data for goodness of fit test

This is a practice question I came across when dong some goodness of fit test examples.A company sells cloths by mail order.The size of clothes is defined by hip size; thus the height of customers of a particular customer may vary considerably. Data set of heights sent in by customers of size 18...
13. ### Proof of constistency of Maximum Likelihood Estimators (MLE)

Hi all, I would appreciate some help comprehending a logical step in the proof below about the consistency of MLE. It comes directly from Introduction to Mathematical Statistics by Hogg and Craig and it is slightly different than the standard intuitive one that makes use of the Weak Law of...
14. ### Need Help Choosing a Textbook

Hi, I'm looking for a textbook/book to let me self-study regression analysis. Some background: I have a research psych background academically (I've done many means-tests, chi-squareds, pearson's r, but always with random subjects/experiments) so I'm not totally new to the material, but...