Problem 4. In a generalization of the birthday problem, consider a box of N tickets. Yousample n tickets with replacement. Let pn be the probability of the event that a duplicateticket appears. Write down an exact expression for pn, and also find an approximation toit using log(1 + x) ≈ x for small x. Then, approximate how large n has to be in order forPn ≥ 0.5 (your answer should be a function of N). What is the value of this function of Nfor N 365?

Given : Box of N tickets Sampled n out of N tickets pn: the probability of the event that a…

Answered: Problem 4. In a generalization of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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I only need B,C, and D
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You are given the following data: X= [1.5, 10.22, 2.4, 5.8, 0.43] What would you choose as the parameter if you were to model this as fe a lognormal distribution? (Enter your answer with up to two digits after the decimal point).
Q.4. Annual depth of precipitation X (cm) is assumed to be lognormally distributed with u-50, o=10. What is the probability of the precipitation to remain in the range of 45 and 62 cm?
Situation 9. Suppose that X has a lognormal distribution with parameters 0 = -2 and ² = 9. Determine the following: 18. P(500 x) = 0.1 20. The variance of X.
Fast
4- If X is an exponential with parameter 1, then 2X is chi-square with 2 degrees of freedom. True O False
QUESTION 3 Suppose there are two football teams A and B. In recent matches Team A has a mean of 1 goal per match and Team B has a mean of 2 goals per match. Suppose that the probability of the number of goals scored by a team obeys a Poisson Distribution In the following questions, give the reasoning behind your answers. You can express some answers in terms of logarithms. Q 3(d) What is the most probable score line? Q 3(e) In a particular match, over how long a time period would the probability of no goals be 20%?
I have problem in the question number #2, but the answer is with the result of question number #1
14. Testing multiple linear restrictions with the F test Suppose a data set of 350 observations (N=350) was analyzed using OLS to examine the factors that influence the salaries of professional baseball players. The regression results are as follows, with standard errors in parentheses: log(salary) = 12.1 + 0.08 years + 0.02 gamesyr + 0.0007 bavg + 0.02 hrunsyr + 0.012 rbisyr (0.25) (0.025) (0.004) (0.002) (0.015) (0.008) where salary = total salary in 2003 years = years in the league bavg = career batting average gamesyr = average games played per year hrunsyr = home runs per year rbisyr = runs batted in per year R = 0.611 SSR = 199.32
Let log M = 5 and log K = -6 %3D %3D a.) log(4) K b.) log VK c.) log(M · K*)
A individual, with a utility function lnW and an initial wealth level W0, is faced with a fair gamble of winning or losing $h (where W0 > h > 0) with 50-50 chance. (a) Is this individual risk averse? Explain.(b) Suppose that the individual is willing to pay up to an amount of f in order to avoid such a gamble. Give the equation that determines f, and solve the equation for f (i.e., express f in terms of W0 and h). (c) Show that f increases as h increases.

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