Let T be a continuous random variable having the following probability density function:Sr() = exp(-++t)if t >0Calculate the failure rate function 7r(t) of a device whose faliure density is distributed as T. (Use the words lambda to denote A). Hint: You can use Equation 1.167 in the coursebook this page (Right click to open in new tab).r(t)=

Given information: The probability density function of the continuous random variable is as given…

Answered: Let T be a continuous random variable…

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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The probability density function (p.d.f.) of a continuous random variable X is defined to be: kx + for 0 < x < 1 f(x) = |0 otherwise, for some constant k. For these problems, please ensure your answers are accurate to within 3 decimals. Part a) Find the value of k that makes the above function a proper p.d.f. Part b) Find E(X).
(c) At a bus stop, there are two buses available (bus numbers 1 and 2). For i = 1,2, the waiting time until bus i arrives is denoted by T;, with T independent of T2, and T; has density function fr. (t) = X, exp(-1;t), t>0.
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…
Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) other
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help please answer in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working
Question 2. A continuous random variable, X has the following probability density function: S(x) = cx² 0sxs10 = 0 otherwise a) Find the value of c. b) Find the mean, median, mode, standard deviation and coefficient of variation. c) Find the probability that X is greater than 3.0 given that X is between 2.0 and 5.0.
Statistics UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS. NO LONG EXPLANATION NEEDED. Answer in 4 decimal places.
Use R to complete the following. R code and R output are requested for solution. Please keep your solution clear and easy to read. Unclear solution will not be grade. O for manual solution. Carry out a simulation experiment to illustrate the central limit theorem when the population distribution is arcsine with probability density function f(x) = 1 T√x(1-x) x = (0, 1). Consider the four sample sizes n = 1, n = 3, n = 5, n = 10, and in each case use 10,000 replications. Note: To simulate a random sample of size n from the arcsine distribution in R, use the command rbeta(n,1/2,1/2).
Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2
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