Assume the continuous RV X , with PDF fx and CDF Fx, measures the lifetime of somesystem or component. The hazard rate function for such a variable is defined asfx (t)P(X >t)fx(t)1 – Fx(t)h(t) :and it measures the propensity of the system to fail shortly after time t, given that ithas survived until time t.(a) Show that the hazard rate function for the Exponential(A) distribution fort > 0 is constant and equal to A (this is equivalent to the memoryless property).(D) Consider the Gamma(a = 2, X) distribution, which arises as the sumof two independent Exponential(A) RVs. Find the hazard rate function for thisdistribution fort>0. (Hint: Use integration by parts for finding the CDF. )

Given that the hazard rate function for a continuous random variable X with PDF fX and CDF FX as…

Answered: Assume the continuous RV X, with PDF fx…

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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The price P of gasoline increases to a maximum and then stays at a fixed price. What is the rate of change dp/dt and how is it changing at the time when the price reaches a maximum?a. dp/dt is negative at the maximum and is decreasing.b. dp/dt is equal to zero at the maximum and remains the same.c. dp/dt is positive at the maximum and is decreasing.d. dp/dt is negative at the maximum and is increasing.
Can you show an example similar to this problem part A - but not this problem - of how to calculate an exact percentage change?
Assume that the demand curve is P = f(Q) = 60 − 0.2Q and the supply curveis P=g(Q) = 30 + 0.3Q. Find the equilibrium price and quantity and also compute consumer and producer surplus by applying integral.
What was the maximum sustained yield under the logistic harvest model when k=500 and r=0.4? Values 1 500 1000 49L K L N N.d num [1:601] 0 123456789... num [1:50] 5 157.502 1079.678 0.732 24.054 ... num [1:50] 114 329 349 350 350 ... 0.4 int [1:50] 1 2 3 45678910 50 t Nt r Z Z L P T time y Files Plots Packages Help Viewer Presentation Zoom Export num [1:601] 0.4 0.399 0.398 0.398 0.397 ... Publish Observed Growth Rate 69 -0.1 0.1 0.3 0.5 Observed Growth Maximum Growth Carrying Capacity 0 100 200 300 400 500 600
The market research department of a company recommends that the company manufacture and market a new calculator. After a comprehensive study on the market, the research department presents the following price-demand equation: 2 = 150 – p where z is the number of calculators that can be sold at a price p pesos. %3D What is the marginal revenue function in terms of z? MCQ1.pdf OR' (x) = -3x2 +150 OR (x) = 150 – x? O R (x) = 150 – 2x OR (x) = -4x + 300x
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A population of fish is living in an environment with limited resources. This environment can only support the population if it contains no more than M fish (otherwise some fish would starve due to an inadequate supply of food, etc.). There is considerable evidence to support the theory that, for some fish species, there is a minimum population m such that the species will become extinct if the size of the population falls below m. Such a population can be modelled using a modified logistic equation: dP =(1-)(-) m dt M
A problem that occurs with certain types of mining is that some byproducts tend to be mildlyradioactive, and these products sometimes get into our freshwater supply. The EPA has issuedregulations concerning a limit on the amount of radioactivity in supplies of drinking water.Particularly, the maximum level for naturally occurring radiation is 5 picocuries per liter ofwater (on average). A random sample of 24 water specimens from a city’s water supply gave ̄x= 4.61 and s = 0.87. Do these data provide sufficient evidence to indicate that the meanlevel of radiation is safe (below the maximum level set by the EPA)? Test usingα= 0.05.

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