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ramj
Questions and answers by visitors named
ramj
Questions (12)
Let π1,β¦,ππ be i.i.d. random variables with distribution ξΊ(π,π) , for some unknown parameter π>0 .
Find an
4 answers
2,906 views
A random variable X is generated as follows. We flip a coin. With probability p , the result is Heads, and then X is generated
3 answers
1,431 views
Let X1,β¦,Xn be i.i.d. Poisson random variables with parameter Ξ»>0 and denote by XΒ―Β―Β―Β―n their empirical average,
XΒ―Β―Β―Β―n
4 answers
2,195 views
Argue that the proposed estimators πΛ and πΛ below are both consistent and asymptotically normal. Then, give their
3 answers
1,936 views
The Gamma distribution Gamma(πΌ,π½) with paramters πΌ>0 , and π½>0 is defined by the density
ππΌ,π½(π₯)=π½πΌ
7 answers
2,632 views
Suppose that the rejection region of a test π has the form π ={πβ―β―β―β―β―π:πβ―β―β―β―β―π>π} . Find
1 answer
493 views
The National Assessment of Educational Progress tested a simple random sample of 1000 thirteen year old students in both 2004
4 answers
1,753 views
a)π1,β¦,ππβΌπ.π.π.π―ππππ(π) for some unknown π>0 ;
π»0:π=π0 v.s.
4 answers
1,449 views
Let π1,β¦,ππ be i.i.d. Bernoulli random variables with unknown parameter πβ(0,1) . Suppose we want to test
π»0:οΏ½
3 answers
asked by
ramj
1,972 views
Let X be a single (i.e. n=1 ) Gaussian random variable with unknown mean ΞΌ and variance 1 . Consider the following hypotheses:
H
4 answers
1,549 views
Suppose that the rejection region of a test Ο has the form R={Xn:Xn>c} . Find the smallest c such that Ο has level Ξ± .
(If
4 answers
1,276 views
Consider an i.i.d. sample X1,β¦,XnβΌPoiss(Ξ») for Ξ»>0 .
Starting from the Central Limit Theorem, find a confidence interval
3 answers
1,287 views
Answers (4)
Suppose that the test Ο has level Ξ±=0.05 . What is the power of Ο ? (If applicable, type abs(x) for |x| , Phi(x) for Ξ¦(x)=P(Zβ€x) where ZβΌN(0,1) , and q(alpha) for qΞ± , the 1βΞ± quantile of a standard normal variable, e.g. enter q(0.01) for q0.01
Using the previous part, find confidence intervals for πΌ with asymptotic level 90% using both the βsolving" and the βplug-in" methods. Use π=25 , and πβ―β―β―β―β―π=4.5 . (Enter your answers accurate to 2 decimal places. Use the Gaussian
clarification : Let π1,β¦,ππ be i.i.d. random variables with distribution N(π,π) , for some unknown parameter π>0 .
Secondly, express P(|Z|β€t) in terms of Ξ¦(r)=P(Zβ€r) for t>0 . Write Phi(t) (with capital P) for Ξ¦(t) .
