Consider a renewal process with the lifetimes X1, X2, ... having the probability density function f(x) = 0.125. (4 — x)for 0 < x < 4.Determine the asymptotic expression for the probability distribution of excess life Yt:lim P(2.75) =t→∞Determine the limiting mean excess life:lim E[Y] =t→∞=

To solve the given problem, there are a series of steps that must be followed. The problem deals…

Answered: Consider a renewal process with the…

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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Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that X has the following probability density function (called the Rayleigh probability density function). (x/0²) e-x²/(20²) x > 0 f(x) = 10 otherwise (a) If = 108, find the probability that the vibratory stress is between 82 and 361. (b) If = 108, then 92% of the time the vibratory stress is greater than what value?
How do you find the 0.603 without using excel. Thank you!
The probability density function of X, the lifetime of a certain type of device (measured in months), is given by if x 24 Find the following: P(X > 40) = The cumulative distribution function of X: if a 24 The probability that at least one out of 6 devices of this type will function for at least 46 months:
If X has the probability density * 21 f(2): 2 <1 Find P (1 < X < 5). Select one: O a. 0.93 O b. 0.96 O G 0.12 O d. 0.91
QI Since h(t) = 1+t 1>0 i. The survival function is given by? ii. Probability density function is given by iii. The mean time to failure(MTTF) of the component is given by
The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is: f(x,x) = 1 e-^x for 0 ≤ x ≤ ∞o, λ = 0.5. λ is what R calls rate. Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts. d) What is the probability that X is greater than its expected value? e) What is the probability that X is > 5? f) What is the probability that X is> 10? g) What is the probability that X > 10 given that X > 5? h) What is the median of X? Please solution USING R script
The normal probability density function g(x) = ov2n Where u = mean, o = standard deviation, n = 3.14159, e 2.71828 Let's study a special case where u = 0 and o = 1, which indicates a standard normal probability density function. For simplicity, we scale the function so as to remove the factor 1/(ov2n). Now, we have a new function f(x) f(x) = e (a) Find f'(x) and show the intervals of increase or decrease for f. (b) Find the extreme value of f. (c) Find the intervals of concavity and the inflection points. (d) Sketch the graph of f and point out the extremum value and inflection points.
Suppose lifetime of a particular type of old mobile, ?, can be modelled by the probability density function............ Answer follow image:
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
Please show every step.
22
1. Given the following probability density function: P(x) = Ae¬^(x-a)². (a) Find (x) (b) Find (x?) (c) Find ox (d) Sketch the graph of the probability density.

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