# Search results

1. ### 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...
2. ### Total and quadratic variation of a function

Let f(x)= x2−3, for x<3, x2+3, for x≥3 I need to determine the total variation and the quadratic variation of f(x) on the interval [−4, 4]. For the total variation, I guess I can use my raw way to do it. It means see that f(−4)=13, f(0)=−3, f(2.999999)=5.99999, f(3)=12, f(4)=19. So...
3. ### Poisson process: phone calls

We assume that phone calls arrive according to a Poisson process with rate 2. If I know that up to time t = 1 there is one call only, how likely is it that it arrived after t = 0.75? If I know that up to time t = 1 two calls arrived, how likely is it that the second arrived after t = 0.75? So...
4. ### Hazard rate of the Pareto distribution

I need to calculate the hazard rate of the Pareto distribution. I know that the residual life distribution looks at the remaining waiting time given that you have already waited for a certain amount of time x, and the hazard rate can be thought of as the likelihood of the wait time ending...
5. ### 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.
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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)
10. ### 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...
11. ### Row problem with mandatory empty seats

Here is the exact question: Suppose that 39 students (you being one of them) are randomly seated in a long row of 120 seats. How likely is it that you will not have a direct neighbor? What I've understood: that one the side you can only have one seat with no neighbor next to you and one...
12. ### Dis./Avantadges of estimating of binary response model with OLS

In the Maximum Likelihood Estimator context, I can't find answers for those two questions: - What are the advantages and disadvantages of estimating of a binary response model with OLS ? - Same questions but compared to MLE ? I thank you in advance :o
13. ### Pooled GLS and POLS

Hello everyone, This semester I'm studying, OLS, GLS, RE, FE, MLE, and a lot of beautiful concepts :D. But I get a little bit concerning the different assumptions of each model and their difference. Here is what I need to answer and I will say what I've understood/found so far thanks my...