If you have a set of samples S= 0, 0, 1, 0, 1, 0 from a binomial distribution where P(x + 0) = 1ji and P(x = 1) = mu , the maximum likelihood estimate of u is
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If you have a set of samples S= 0, 0, 1, 0, 1, 0 from a binomial distribution where P(x + 0) = 1ji and P(x = 1) = mu , the maximum likelihood estimate of u is
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- The interval (3, 15) is the 95% confidence interval for a population parameter µ from a random sample of size 25, where the random sample is drawn from a normal Find the lower limit for the 90% confidence distribution with unknown variance o interval for the population mean uYou decide to play K number of video games, where K is a Poisson random variable with parameter d. Assume that time you spend on a video game k = 1,2,..., K has a normal distribution with mean 4, and variance of. Also assume that 4k >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.Suppose X₁,, Xn from a normal distribution N(μ, o²) where both μ and o are unknown. We wish to test the hypotheses Ho: o² = o vs. Ha: 0² # of at the level a. Show that the likelihood ratio test is equivalent to the x² test.
- You decide to play K number of video games, where K is a Poisson random variable with parameter A. Assume that time you spend on a video game k = 1, 2,..., K has a normal distribution with mean µg and variance of. Also assume that µk >> 0 and of is small, so that you can neglect negative time values. Let T be the total time you spend on playing video games, compute the mean and variance of T.Suppose the random variable, X, follows a geometric distribution with parameter (0< 0 <1). Let X₁, X₂, X, be a random sample of size n from the population of X. (d) Find the method of moments estimator (mme) of 0. (e) Show how the mle of 0 is related to its mme. Explain if it is always true. (f) Verify if X, is a sufficient statistic for 8 or not. (g) Justify if = is an unbiased estimator for 6.This column contains data x1, . . . , xn, which is assumed to be a sample from a normal distribution N(µ, σ 2 ). For this sample, find the maximum likelihood estimates µˆ and σˆ.
- i need help with cSuppose we obtain n observations from a sinusoid contaminated by Gaussian noise: X = A· sin(2 · T· f·k+¢) + Wk, k = 1, 2, ...,n, %3D where Wg are independent identically distributed (iid) Gaussian random variables with mean o and variance o?. The frequency f and phase o are known constants, while A is an unknown constant. Find the maximum likelihood estimator for A. Show all work.if we determine that a problem follows a geometic distribution, show that the probability of a success on the first trial is equal to P. Then, show the sequence of the first five terms as we increase X from 1 to 5
- Assume that a random variable Y has a mean of zero and standard deviation of one. Calculate the expected value of X1 and X2 if they are defined as below. X1 = Sigma+ Mu X2 = Sigma(Y+Mu)You obtain 336 successes in a sample of size n1=391n1=391 from the first population. You obtain 419 successes in a sample of size n2=472n2=472 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sampleThe amount of gasoline in gallons sold by three different gas stations during one day is given by the independent random variables X1,X2, X3 each with a normal distribution. X1 has a mean µl =700 and standard deviation ơ1 55; X2 has mean u2 =700 and standard deviation o2 = 65; X3 has mean u3=900 and standard deviation 03 = 100. Suppose the prices per gallon are $2.90, $3.00 and $3.10 for X1, X2, and X3 respectively. Find the probability that the combined revenue for a given day is less than $6000. Use the z-score table. Round answer to the nearest hundredth.
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