Reference no: EM13985524
1. Let X1,..., Xn be a random sample from an N(μ, σ2).
(a) Construct a (1 - α)100% con?dence interval for μ when the value of σ2 is known.
(b) Construct a (1 - α)100% con?dence interval for μ when the value of σ2 is unknown.
2. Let X1,..., Xn be a random sample from an N(μ1, σ2) population and Y1,..., Yn be an independent random sample from an N(μ2, σ2) distribution where σ2 is assumed to be known. Construct a (1 - α)100% interval for (μ1 - μ2). Interpret its meaning.
3. Let X1,..., Xn be a random sample from a uniform distribution on [θ, θ + 1]. Find a 99% con?dence interval for θ, using an appropriate pivot.
|
Taxable bonds offer a rate of return
: Consider a real estate project. It costs $1,000,000. Thereafter, it will produce $60,000 in taxable ordinary income before depreciation every year. Favorable tax treatment means that the project will produce $100,000 in tax depreciation write-offs ea..
|
|
Mean instead of the median
: Even though both X and M are unbiased, the reason we usually use the mean instead of the median as the estimator of μ is that X has a smaller variance than M.]
|
|
Problem regarding the unbiased estimator
: Let X1,..., Xn be a random sample from a population with the mean μ. What condition must be imposed on the constants c1, c2,..., cn so that c1X1 + c2X2 + ··· + cnXn is an unbiased estimator of μ?
|
|
Con?dence interval for the mean
: Find a 98% con?dence interval for the mean P/E multiples. Interpret the result and state any assumptions you have made.
|
|
Random sample from a uniform distribution
: Let X1,..., Xn be a random sample from a uniform distribution on [θ, θ + 1]. Find a 99% con?dence interval for θ, using an appropriate pivot.
|
|
Calculating a con?dence interval
: 1. (a) Suppose we construct a 99% con?dence interval. What are we 99% con?dent about? (b) Which of the con?dence intervals is wider, 90% or 99%? (c) In computing a con?dence interval, when do you use the t-distribution and when do you use z, with nor..
|
|
Time between successive arrivals
: Let X be a random variable representing the time between successive arrivals at a checkout counter in a supermarket. The values of X in minutes (rounded to the nearest minute) are
|
|
Resulting from tossing a coin
: Let X1,..., Xn be a random sample recorded as heads or tails resulting from tossing a coin n times with unknown probability p of heads. Find the MLE pˆ of p. Also using the invariance property, obtain an MLE for q = 1 - p. How would you use the re..
|
|
Method of moments to ?nd a point estimator
: Let X1,..., Xn be a random sample of size n from the geometric distribution for which p is the probability of success. (a) Use the method of moments to ?nd a point estimator for p.
|