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UCLA Statistics, Neurology, LONI, Math/PIC

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STAT 35 Spring 2008	*Interactive and Computational Probability*
Department of Statistics	Instructor: Ivo Dinov
Homework 5	Due Date: Friday, June 06, 2008

Please, submit your homework before class on the due date. See the HW submission rules. On the front page include the following header.

(HW_5_1) Consider writing onto a computer disk and then sending it through a certifier that counts X, the number of missing pulses. Suppose this number X has a Poisson distribution with parameter λ = 0.25. Run the Poisson Experiment under the SOCR Experiments and calcualte emperically (by running 100, 1,000 or more experiments) and theoretically (by using the Poisson probability formula) each of the following probabilities.

(HW_5_2) The Pareto family of distributions (see SOCR Distributions) has been used to approximate the distribution of income, city population size, size of firms, among others. The Pareto distribution has two parameters, k and ϑ, both strictly positive, and its pdf is defined by:

		\|	kϑ^k / x^k+1	x≥ϑ
f(x; k, ϑ)	=	\|
		\|	0	x<ϑ

f(x; k, ϑ)

(HW_5_3) Suppose the diameter at breast height of trees (in.) of a certain type is Normally distributed with µ = 8.8 and σ = 2.8. Use the Normal Distribution Modeler part of SOCR Distributions to compute the following probabilities.

in.

(HW_5_4) The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is measured on a continuous scale and is Normally distributed with mean 70 and standard deviation 3. Use the Normal Distribution Modeler part of SOCR Distributions to compute the following:

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