Suppose X1, . . . , XM is a set of M observations representing the Binomial...

Suppose X1, . . . , XM is a set of M observations representing the Binomial probability model.

please explain and write neatly so I can understand..

(a) Write out the likelihood function.

(b) Write out the log-likelihood function.

(d) Set the score function equal to zero and solve for the parameter p.

(e) Take the second partial derivative of the score function.

(f) Check to make sure this value is negative to ensure that the log-likelihood function is concave down.

(g) What is the Maximum Likelihood estimator for a Binomial probability model?

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with...

Suppose that X1, X2, , Xm and Y1, Y2, , Yn are independent random samples, with the variables Xi normally distributed with mean μ1 and variance σ12 and the variables Yi normally distributed with mean μ2 and variance σ22. The difference between the sample means, X − Y, is then a linear combination of m + n normally distributed random variables and, by this theorem, is itself normally distributed. (a) Find E(X − Y). (b) Find V(X − Y). (c)...

A sample of 120 observations indicated that X1 is 77. A second sample of 153 observations...

A sample of 120 observations indicated that X1 is 77. A second sample of 153 observations indicated that X2 is 89. Conduct a z-test of hypothesis about a difference in population proportions using a 0.05 significance level. H0: p1 - p2 = 0 H1: p1 - p2 ≠ 0 a) State the decision rule. Reject H0 in favour of H1 if the computed value of the statistic is between -1.96 and 1.96. Reject H0 in favour of H1 if the...

A sample of 103 observations indicated that X1 is 93. A second sample of 155 observations...

A sample of 103 observations indicated that X1 is 93. A second sample of 155 observations indicated that X2 is 82. Conduct a z-test of hypothesis about a difference in population proportions using a 0.02 significance level. H0: p1 - p2 ≥ 0 H1: p1 - p2 < 0 a) State the decision rule. Reject H0 in favour of H1 if the computed value of the statistic is between -2.33 and 2.33. Reject H0 in favour of H1 if the...

A sample of 112 observations indicated that X1 is 100. A second sample of 146 observations...

A sample of 112 observations indicated that X1 is 100. A second sample of 146 observations indicated that X2 is 97. Conduct a z-test of hypothesis about a difference in population proportions using a 0.04 significance level. H0: p1 - p2 = 0 H1: p1 - p2 ≠ 0 a) State the decision rule. Reject H0 in favour of H1 if the computed value of the statistic is less than 2.05. Reject H0 in favour of H1 if the computed...

Suppose you have one data set with 30 cases, each case representing a student in this...

Suppose you have one data set with 30 cases, each case representing a student in this class. The following variables are available: age, gender/sex, race/ethnicity, class (freshman, sophomore, etc.), and GPA. For each of the 5 variables, explain (1) the level of measurement and (2) the measures of central tendency available to them. Race: Gender/sex: Race/ethnicity: Class: GPA:

For a set of ungrouped or individual observations, the sum of the deviations of all observations...

For a set of ungrouped or individual observations, the sum of the deviations of all observations from the mean is: a. the standard deviation b. the interquartile range c. the median d. zero e. the sum of all the observations

Suppose we have a random sample of n observations {x1, x2, x3,…xn}. Consider the following estimator...

Suppose we have a random sample of n observations {x1, x2, x3,…xn}. Consider the following estimator of µx, the population mean. Z = 12x1 + 14x2 + 18x3 +…+ 12n-1xn−1 + 12nxn Verify that for a finite sample size, Z is a biased estimator. Recall that Bias(Z) = E(Z) − µx. Write down a formula for Bias(Z) as a function of n and µx. Is Z asymptotically unbiased? Explain. Use the fact that for 0 < r < 1, limn→∞i=1nri...

1. For a data set with 3 variables and 3 observations, suppose Xbar, the sample mean...

1. For a data set with 3 variables and 3 observations, suppose Xbar, the sample mean vector is [5, 3, 4]’. Let b’ = (1 1 1) and c’ = (1 2 -3). The sample covariance matrix is given as, S = ( 13 −3.5 1.5; −3.5 1 −1.5 ; 1.5 −1.5 3 ) (a) Find the sample mean and variance for b’X and c’X. (b) Find the sample mean and variance for c’X. (c) Find the covariance between b’X and...

Suppose there are 2 goods, x1 and x2. The price of x1 goes up. x1 is...

Suppose there are 2 goods, x1 and x2. The price of x1 goes up. x1 is inferior, and x2 is normal. Using income and substitution effects, show which of the claims below is correct. Question options: x1 will decrease in quantity, but x2 will go up x1 may increase or decrease in quantity, the same is true for x2 the quantity of both goods will go down the quantity of both goods will go up

Consider the following matched samples representing observations before and after an experiment. Assume that the sample...

Consider the following matched samples representing observations before and after an experiment. Assume that the sample differences are normally distributed. Use Table 2. Before 2.5 1.8 1.4 -2.9 1.2 -1.9 -3.1 2.5 After 2.9 3.1 3.9 -1.8 0.2 0.6 -2.5 2.9 Let the difference be defined as Before – After. a. Construct the competing hypotheses to determine if the experiment increases the magnitude of the observations. H0: μD = 0; HA: μD ≠ 0 H0: μD ≥ 0; HA: μD...

Subjects