5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102)....

Question

Question

5. Let X1, X2,... , X100 be i.i.d. random variables, following the normal distribution N(0, 102). Let α denote the probabilit

Answer 1

Answer #1

fue r) me too. -thero uhose Noo 19.6 P= o, 05 . P 0.0S autor Here y fi -h of vaiables ha Plyz) an erro leu -than o-ol ástoaiq to poisson

Answer 2

Similar Homework Help Questions

Let X1, X2 · · · X10 be i.i.d. random variables. And all of them have...

Let X1, X2 · · · X10 be i.i.d. random variables. And all of them have the distribution uniform[0, 2]. Please calculate the variance of the 2nd largest number among these X’s.
Problem 3: Suppose X1, X2, is a sequence of i.i.d. random variables having the Poisson distribution...

Problem 3: Suppose X1, X2, is a sequence of i.i.d. random variables having the Poisson distribution with mean λ. Let A,-X, (a) Is λη an unbiased estimator of λ? Explain your answer. (b) Is in a consistent estimator of A? Explain your answer 72
7. Let X1, X2,.. be i.i.d. random variables, and let T(t)minn: X > t, t20. (a)...

7. Let X1, X2,.. be i.i.d. random variables, and let T(t)minn: X > t, t20. (a) Determine the distribution of T(t) (b) Show that, if p= P(X1> t)0 astoo, then pT(t)Exp(1) as to 7. Let X1, X2,.. be i.i.d. random variables, and let T(t)minn: X > t, t20. (a) Determine the distribution of T(t) (b) Show that, if p= P(X1> t)0 astoo, then pT(t)Exp(1) as to

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...

3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What is the distribution of N? (b) Find the conditional distribution of (X1, X2, X3) | N. (c) Now let N, X1, X2, X3, be random variables such that N~ Poisson(A), (X1, X2, X3) | N Trinomial(N; pi,p2.ps) where pi+p2+p3 = 1. Find the unconditional distribution of (X1, X2, X3). 3. (25 pts.) Let X1,...
24. Let X1, X2, ...., X100 be a random sample of size 100 from a distribution...

24. Let X1, X2, ...., X100 be a random sample of size 100 from a distribution with density for x = 0,1,2, ..., otherwise. What is the probability that X greater than or equal to 1?
26./ Let Xi, X2, X100 be i.i.d. Poisson (5) distributed. a./ Find the probability that Sioo...

26./ Let Xi, X2, X100 be i.i.d. Poisson (5) distributed. a./ Find the probability that Sioo is bigger than 550. b./ Find the probability that S100 is bigger than 5.2

5. Let X1, ..., X 100 be i.i.d. random variables with the probability distribution function f(x;0)...

5. Let X1, ..., X 100 be i.i.d. random variables with the probability distribution function f(x;0) = 0(1 - 0)", r=0,1,2..., 0<o<1 Construct the uniformly most powerful test for H, :0= 1/2 vs HA: 0 <1/2 at the significance level a =0.01. Which theorems are you using? Hint: EX = 1, VarX = 10.
7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n...

7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n >0 in probability if nP(Xn > n) -» 0. (b) Find a random variable Y satisfying nP(Y > n) ->0 and E(Y) = Oo
Let λ >0 and suppose that X1,X2,...,Xn be i.i.d. random variables with Xi∼Exp(λ). Find the PDF...

Let λ >0 and suppose that X1,X2,...,Xn be i.i.d. random variables with Xi∼Exp(λ). Find the PDF of X1+···+Xn. Use convolution formula and prove by induction

(2) Let X1,X2 be i.i.d. Poisson () random variable. Is X+X2 or X, + 2X2 sufficient...

(2) Let X1,X2 be i.i.d. Poisson () random variable. Is X+X2 or X, + 2X2 sufficient for? Why? Find the MVUE of X