30. If e1+81' is the moment generating function of a normal variate X, find P(-1< X <9).
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- The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.If n is 30 and p is 0.04. using the Poisson approximation to the Binomial, the P(X < 2) is equal to a 0.4101 b. 0 .2103 C 0.0867 d. 0 .8795
- Suppose X1, X2, ... , Xn is a random sample and Xi = {1, with probability p 0, with probability 1-p} for every i = 1, 2, ... , n. Find the Moment Generating Function of ∑i=1n Xi . What is the distribution of ∑i=1n Xi ?they take samples of 4 fireworks for quality co from and examine them for defects. let X be the number of defective fireworks in the sample of 4.An SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0 : pS – pH 0, Ha : pS – pH 0. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? a. If the on-time rates for the two airlines are equal, there is a 0.0117 probability of getting samples with a difference as far or farther from zero as these samples. b. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. c. The probability of making a Type I error is 0.0117. d. The probability of making a Type II error…
- Suppose X is binomially distributed with parameters n and p; further suppose that E(X) = 5 and Var(X) = 4. Find the n and p.Suppose that X has a Poisson distribution with h = 80. Find theprobability P(x is less than or equal to 80)Let X1,...Xn be iid Poisson(λ1) and Y1,...,Ym be iid Poisson(λ2). Write out the GLRT for testing H0: λ1 = λ2 versus Ha: λ1 ≠ λ2.
- Suppose the math tutoring lab sees 56 students on a typical Tuesday and that the number of students per day is Poisson distributed. a. Find P(X ≤ 43). What function or formula did you use to answer this question? On my TI-84 Plus, I did a PoissonCDF with Lambda = 56 and the x value = 43. This resulted in 0.04309... Was I correct in using the PoissonCDF, or should I have used the PoissonPDF? b. What is the probability that more than 60 students will come in next Tuesday? Likewise, on my TI-84 Plus, I did a PoissonCDF with Lambda = 60 and the x value = 56. This resulted in 0.7309... Was I correct in assuming that the Lambda is 60 and the x value is 56?Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. n = 4, x = 2. n = 4, x = 4Let m(t) be the moment generating function of a random variable X. Show that the random variable W = 10X is m(10t). What is the moment generating function of Z = X-5 in terms of m(t)?
