## Probability and Distribution Theory

How many different 5 card poker hands can be dealt from a deck of 52 cards There are I 5 I 2,598,960 possible hands. 2. Compute the probability of being dealt 4 of a kind in a poker hand. There are 48(13) possible hands containing 4 of a kind and any of the remaining 48 cards. Thus, given the answer to the previous problem, the probability of being dealt one of these hands is 48(13) 2598960 .00024, or less than one chance in 4000. 3. Suppose a lottery ticket costs 1 per play. The game is played...

## Models for Panel Data

The following is a panel of data on investment (y) and profit (x) for n 3 firms over 7 10 periods. i 1 i 2 i 3 (a) Pool the data and compute the least squares regression coefficients of the model yit a+ P'x,j + sii. (b) Estimate the fixed effects model of (13-2), then test the hypothesis that the constant term is the same for all three firms. (c) Estimate the random effects model of (13-18), then carry out the Lagrange multiplier test of the hypothesis that the classical model without the...

## Functional Form and Structural Change

In Solow's classic 1957 study of technical change in the U.S. Economy, he suggests the following aggregate production function q t A t f k t where q t is aggregate output per manhour, k t is the aggregate capital labor ratio, and A t is the technology index. Solow considered four static models, q A a plnk, q A a - p k, ln q A a plnk, ln q A a - p k. He also estimated a dynamic model, q t A t - q t-1 A t-1 a pk. b Solow's data for the years 1909 to 1949 are listed in Table A8.1 Op. cit., page...

## Inference and Prediction

A multiple regression of y on a constant, x1, and x2 produces the results below y 4 ,4xi .9x2, R 8 60, e' e 520, n 29, X'X The estimated covariance matrix for the least squares estimates is the test may be based on t .4 .9 - 1 .410 .256 - 2 .051 1 2 .399. This is smaller than the critical value of 2.056, so we would not reject the hypothesis. 2. . Using the results in Exercise 1, test the hypothesis that the slope on x1 is zero by running the restricted regression and comparing the two sums...