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Results tagged with self-study
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user 284757
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.
0
votes
1
answer
105
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Calculational of conditional expectations
Let $X$ and $Y$ be iid random variables, with $P(X=k)=2^-k$ for $k=1,2,3.....$. Find $P(X>Y)$ and $P(X>2Y)$.
I solved this question by applying transformations and got $P(X>Y)=2/3$ and $P(X>2Y)=1/(4(2 …
- 124
3
votes
2
answers
1k
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Sufficient statistic of Bernoulli Trial
Let $X_1$ and $X_2$ be iid random variables from a $Bernoulli(p)$ distribution. Verify if the statistic $X_1+2X_2$ is sufficient for $p$.
I calculated and found out $X_1+X_2$ as a sufficient statistic …
- 124
0
votes
0
answers
94
views
Binomial distribution mixed with geometric distribution
Suppose X is the number of heads in 10 tosses of a fair coin. Given X=5, what is the probability that the first head occurred in the third toss?
We can assume X to a Binomial distribution with p=1/2 a …
- 124
0
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0
answers
103
views
Calculating consistent estimators
Let $X_1, X_2,\dots$ be $iid$ random variables with density $f(x|p), 0<p<1$ being the unknown parameter. Suppose that there exists an unbiased estimator T of $p$ based on sample size 1, i.e. $E(T(X_1) …
- 124