to searchA random variable X has probability density functionf (x;0) =Oe-Ox, x > 00, elsewhereIt is desired to test the null hypothesis H:0=1 against the alternative H₁:0=2.1Which of the following statements is incorrecta=0.6065 if His rejected at X11-ß=0.6321 if His rejected at X ²2All of the above2Click Save and Submit to save and submit. Click Save All Answers to save all answers.Ata

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Answered: A random variable X has probability…

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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Suppose that a random variable X measures the lifetime of a phone battery indays. Suppose its probability density function is:f(x) = (3x^2) if 0 < x < 1 0, otherwiseWhat is the probability that of 30 such types of devices, at least 26 will function for at least 0.5 days? You may assume the batteries are independent of each other. Please compute your answer to four decimal places.
Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
According to the Maxwell–Boltzmann law of theoret-ical physics, the probability density of V, the velocity of a gas molecule, isf(v) =⎧⎨⎩kv2e−βv2for v > 00 elsewhere where β depends on its mass and the absolute tem-perature and k is an appropriate constant. Show that the kinetic energy E = 1 2mV2, where m the massof the molecule is a random variable having a gammadistribution.
Suppose that X is a random variable with density and suppose that ?=e(-4X) Determine ?(?)
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.
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 manager of a stockroom in a factory has constructed the following probabilitydistribution for the daily demand (number of times used) for a particular toolY 0 1 2P(y) 0.1 0.5 0.4It costs the factory $10 each time the tool is used. Find the mean and the variance ofthe daily cost for use of the tool. (b) A random variable X has a probability density function ⎩⎨⎧ − ≤ ≤ = otherwiseAx x x f x0,(6 ) ,0 6 ( ) 2 (i) Find the value of the constant A(ii) Calculate E(X) , mode and the var(X) (c) A certain manufacturing process yields electrical fuses of which, in the long run15% are defective. Find the probability that in a random sample of size n=10, fusesselected from this process, there will be(i) No defective fuse(ii) At least one defective fuse(iii) Exactly two defective fuses(iv) At most one defective fuse (d) The number of errors in a text book follows a Poisson distribution with mean of0.01 errors per page. What is the probability that there are three or less errors in100pages? (e)…
In certain experiments, the error made in determiningthe density of a substance is a random variable having auniform density with α = −0.015 and β = 0.015. Find theprobabilities that such an error will(a) be between −0.002 and 0.003;(b) exceed 0.005 in absolute value.
If the random variable T is the time to failure of a commercial product and the values of its probability den-sity and distribution function at time t are f(t) and F(t), then its failure rate at time t is given by f(t)1 − F(t). Thus, thefailure rate at time t is the probability density of failure attime t given that failure does not occur prior to time t.(a) Show that if T has an exponential distribution, thefailure rate is constant. (b) Show that if T has a Weibull distribution (see Exer-cise 23), the failure rate is given by αβt β−1.
Let X1, X2 .....Xn be n i.i.d. Γ(2,β) random variables where β is unknown, and the probability density function of each Xi is given by (in first screenshot) where Γ(2)=1. i) Show that the maximum likelihood estimator (MLE) βˆof β is given by βˆ = on second screenshot. ii) Now find a consistent estimator of β. Justify your answer. Γ is gamma.
Suppose that the joint density function of the random variables X and Y is f(x,y)=k(1+2y), if 7<x<13 and 0<y<1, and f(x,y)=0, otherwise. Show that the marginal distribution of X is g(x)=c, if 7<x<13, and g(x)=0 otherwise. Enter the value of c. Hint: Of course, first, you need to find the value of k. Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03. (Do NOT use decimal comma; 0,03 would be wrong.)

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