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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.

3 votes
2 answers
1k views

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 …
Nisha's user avatar
  • 124
0 votes
1 answer
105 views

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 …
Nisha's user avatar
  • 124
0 votes
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) …
Nisha's user avatar
  • 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 …
Nisha's user avatar
  • 124