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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 …
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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 …
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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 …
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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 …
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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 …
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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 …
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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 …
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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 …
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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 $E(XY) = E(X^2)$ …
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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 …
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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 …
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