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Suppose X~bin(n 20, p = .4). Derive the closed form (i.e. no long sum) for Mr(t)
and are independent what is the distribution of Y=X1+X2 X~ bin(n,p) We were unable to transcribe this image
find a closed form solution to recurrence relation xn = n for 0 n < m and xn = xn-m+ 1 for n m discrete math We were unable to transcribe this imageWe were unable to transcribe this image
consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)ds We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image tg p(s)ds
Let X(t) = 2; if 0 t 1; 3; if 1 t 3; -5; if 3 t 4: or in one formula X(t) = 2I[0;1](t) + 3I(1;3](t) - 5I(3;4](t). Give the Itˆo integral X(t)dB(t) as a sum of random variables, give its distribution, specify the mean and the variance. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
Question 4. Suppose for i=1,...,n both the mean and variance are unknown. Based on n=100 sample data, we would like to test vs a) at a type 1 error level , find a sample statistic T and the rejection region R that correctly controls exactly, i.e., find T and R that satisfy (must be exact in distribution not approximate). b) Compute the asymptotic power of T, i.e., what does converge to as sample size goes to infinity? Question 5. Following...
4. (20 pts.) [Bonus Question) Suppose that X is a Binomial RV with p=0.5 i.e. X ~ Bin(n,0.5). Find the probability mass function of the transformation Y = 2X.
Suppose N has a geometric distribution with parameter p Derive a closed form expression for E N I N <= k), k = 1,2 . Check via simulaton for p = 0.2, k = 3 Suppose N has a geometric distribution with parameter p Derive a closed form expression for E N I N
Suppose constitute a random sample drawn from a population N(, ) and constitute a random sample drawn from another population N(, ). The two samples are drawn independently. Derive a generalised likelihood ratio test for testing against where and are positive constants such that > . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageμ2 We were unable to transcribe this imageWe were unable...
Consider a binomial experiment with n = 15 and p = 0.1. a.Compute f(0) (to 4 decimals). b.Compute f(14) (to 4 decimals). c.Compute P(x 3) (to 4 decimals). d.Compute P(x 4) (to 4 decimals). e.Compute E(x). f.Compute Var(x) (to 1 decimal) and (to 2 decimals). Var(x) = (to 2 decimals) = ( to 2 decimals) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Suppose X1,··· ,Xn are i.i.d. with pdf if 0 < x < 1 and 0 otherwise. (a) Construct the MP test for the hypothesis v.s. with α=0.05. (b) Derive the power function of the test in (a). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image