The time between successive arrivals of buses may be modelled by a distributionwhose density function is**f(x)20²(x+0) ³'x > 0.If I arrive at the bus stop just as one bus is leaving, what is the probability thatI have to wait at least x minutes for the next one?Suppose that I have already been waiting for c minutes, where c < x. Find theprobability that I have to wait at least x minutes altogether.

Given that the time between successive arrivals of buses is modeled by a distribution with density…

Answered: The time between successive arrivals of…

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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Suppose the duration (in hours) of a certain valve is a random variableX with density function f(x) = 648x−4 for x > 6, and zero otherwise. What's the time expected life (in hours) of this valve?
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The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?
I was calculating a conditional density function and I got an answer of 2x+3y all over 2x+3/2. When I checked the answer, it was 4x+6y all over 4x+3. Those two answers are the same, but my question is--is there some protocol as far as what is proper form to express an answer in when dealing with density functions?
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It is known that the length of time X (in hours) it takes for pizza to be delivered by Domino’s Pizzza hasthe probability density function:f(x) = (12(x^2 − x^3) when 0 < x < 1, and 0 otherwise.a) Find the probability that it will take more than 20 minutes for a pizza to be delivered.b) Find the probability that it will take less than 40 minutes for a pizza to be delivered.c) If 10 independent deliveries are made on a particular day, what is the probability that exactly 7 of them took more than 20 minutes.
Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION
A bottling company produces bottles of fruit juice that are filled, onaverage, with 32 ounces of juice. Due to random fluctuations in the machinery, the actual volume of juice is normally distributed with a standarddeviation of 0.4 oz. Let P be the probability of a bottle having less than31 oz. Express P as an integral of an appropriate density function andcompute its value numerically.
8. Show that the gamma density function f(x, λ, r) integrates to 1

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