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A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
2
votes
Find the distribution parameters
Here are some hints that will hopefuly guide you to the answers.
The expectation $E(T)$ can be obtained using the linearity properties of the expected value.
The variance $\mbox{var}(T)$ can be obta …
4
votes
Accepted
Probability of Largest Sample Observation
There is just a small mistake in the development provided in the question. The mistake comes from the fact that
$$
P(Y > y) \neq P(X_1 > y) \cdot P(X_2 > y) \cdot P(X_3 > y) .
$$
Here is a way to solv …
2
votes
Two easy probability tasks
Since the question is flagged as self-study, I'll just provide some hints to (hopefully) help you derive the solution. I'll amend/complete my answer based on your progress.
Question 1
As a starting …
6
votes
Expected sum of money
The exact probability can easily be computed with the binomial distribution.
Let $X$ be a binomial random variable corresponding to the number of tails obtained in the 1000 tosses.
You could do the f …
30
votes
Accepted
How do I calculate the variance of the OLS estimator $\beta_0$, conditional on $x_1, \ldots ...
This is a self-study question, so I provide hints that will hopefully help to find the solution, and I'll edit the answer based on your feedbacks/progress.
The parameter estimates that minimize the s …
2
votes
How to calculate ${\rm Pr}(F_A|F_B)$ or ${\rm Pr}(F_A| F_B, F_C, F_D)$ in a four node network?
Since this a self-study question, I will provide some hints that will hopefully be usefull.
Use a more useful notation (in my opinion). For each node $k \in \{A, B, C, D \}$, let $I_k$ be a binary r …
2
votes
Compute expectation of a random variable given the density function
If I understood your question correctly, you want to compute ${\rm E}(W)$.
Here are two hints:
Use the property of lineary of the expectation to write ${\rm E}(W)$ as a function of $T$ and 12.
Compu …
1
vote
Normal curve probability mean
Since the question is flagged as self-study, I'll just provide some hints to (hopefully) help you derive the solution. I'll amend/complete my answer based on your progress.
As a starting point, you m …
2
votes
Accepted
Expected value of multiplication of Identically distibuted random variables
It seems that the only situation where the statement is true is when $X = Y$, assuming that $E(X^2) < \infty$.
Indeed, assuming that $X$ and $Y$ are identically distributed, and that $E(XY) = E(X^2)$ …
0
votes
Accepted
Marginalisation on conditional probability
The question seems to by a self-study question. For the moment I'll provide hints that will hopefully lead to the correct expression.
Assuming that $P(O_1 = o_j) > 0$ and by the definition of condit …
1
vote
Correlation influence on two variable coefficients
The variance of $\hat{B}_1$ is
$$
{\rm var}(\hat{B}_1) = \sigma^2 ([X^{'}X]^{-1})_{22},
$$
where $\sigma^2 = {\rm var}(e)$, and $X = [\boldsymbol{1}, X_1, X_2]$
denotes the design matrix (see for exam …