From when I first arrive at the station in the morning, the time T (in minutes) until the train comes isa continuous random variable with density function f(t) = (1/15) exp(-t/15), t > 0. Calculatethe probability that I have to wait between 15 minutes and 30 minutes for the train to arrive.Choose the correct answer out of the following:8.Select one:O 0.0856FinisO 0.6321TimeO 0.9817O 0.2325Check16°C3Type here to search19hpf12insprt scfef7f86JLD

Answered: Image /qna-images/answer/46a6c15d-41a6-4b8e-8b2f-04fa326a6c23.jpg

Answered: From when I first arrive at the station…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the probability that the random variable is between the mean and 1 standard deviation above the mean The length of time (in years) until a particular radioactive particle decays is a random variable t with probability density function defined by ƒ(t) = 4e-4t for t in [0, ∞].
For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
Let Y1 = 0.5, Y2 = 0.25, Y3 = 0.75, Y4 = 0.25 and Y5 = 1.25 be a random sample of width 5 selected from the population with the following probability density function. Which of the following is the estimation value obtained by the moment method for the unknown q parameter of this population?
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?
Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density function. f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. What is the probability that the air temperature will be less than 20˚C (so X ≤ 0.5) and it will take no more than 0.2 minute for the engine to warm up?
Let Y be a random variable whose density function is 3y2 ? y3? f(y|θ)= θ3 exp −θ3 , y>0,where θ > 0 is a parameter. Using an appropriate pivotal quantity, verify that?Y,Y? (− log α)1/3 (− log(1 − α))1/3is a confidence interval for θ with coverage probability 1 − 2α.
Suppose X and Y are independent and identically distributed (i.i.d.) randomvariables, each with the uniform distribution on [0, 1]. What is the cumulative distributionfunction and the density function of XY ?
Find a value of k that will make f a probability density function on the indicated interval. ƒ(x) = kx; [0, 5]
Find a value of k that will make f a probability density functionon the indicated interval.ƒ(x) = kx; [0, 3]
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. What is P(X ≤ 4)? What is P(4.5 < X)?
1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density

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