Consider the Rayleigh distribution below. a) find the hazard rate. b) find the cumulative failure probability....
Question #1 Failure distribution function for a given motor is shown below 10 (a) Derive and sketch the failure density function (8 marks) b) Derive and sketch the and sketch the reliability function (6 marks) (c) Derive and sketch the hazard rate function (6 marks) (d) Would you recommend a burn in period for this motor, why or why not? (4 marks) (e) What is the probability a new molor will last more than 2 years? (4 marks) Determine the...
Time to failure of a household refrigerator. The time to failure
of a particular refrigerator type is represented by the following
pdf: , which is valid within 0 ≤ t ≤ 10 yr, and f(t) = 0 elsewhere.
a) Write the expression for R(t), integrate over t from t to
infinity (which here is 10), and obtain the cumulative Reliability
function, R(t). Then calculate the reliability for the first year,
t = 1. Round your calculated value to 2 sd...
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
Cumulative distribution function The probability distribution of a discrete random variable X is given below: Value x of X P(x-x) 0.24 0.11 -2 0.26 0.11 Let Fx be the cumulative distribution function of X. Compute the following: X 5 ? 18+ (-2) - Px (-4) = 0
Please answer all the way through g.
Time to failure of a household refrigerator. The time to failure
of a particular refrigerator type is represented by the following
pdf: , which is valid within 0 ≤ t ≤ 10 yr, and f(t) = 0 elsewhere.
a) Write the expression for R(t), integrate over t from t to
infinity (which here is 10), and obtain the cumulative Reliability
function, R(t). Then calculate the reliability for the first year,
t = 1....
3. Classifying Life Distributions. Suppose a continuous lifetime T has survival function S(O), hazard function h(i), cumulative hazard function (1), and mean residual life m(t). Consider the following properties that I might have: I. h(t) is nondecreasing for 120, called increasing failure rate (IFR). II. HIV/1 is nondefreasing for >0, called increasing failure rate on the average (IFRA). II. ml) Sm(0) for all / 20, called new better than used (NBU). IV. m(1) decreases in 1, called decreasing mean residual...
Let X be a random variable with cumulative distribution function(a) Find the probability density function fX(x), (b) Find the moment generating function MX(s) for s < 3, (c) Find the mean and variance of X.
X is uniform on (−5, 8) (a) Find P(X^2 > 4). (b) Find the cumulative distribution function of X^2 . (c) Find the probability density function of X^2 . (d) Use the pdf you just found to find Var(X^2 )
----JAVA IMPLEMENTATION URGENTLY NEEDED ------ //Ques 3 /** * Computes the standard Rayleigh distribution probability density function (The mathematical function describing the standard Rayleigh distribution is given by: y = [ x / (σ)^2 ] * e ^ [ (-x^2) / (2σ^2) ] where σ =sigma is the scale variable of Rayleigh distribution. The function y is called the probability density function of the standard Rayleigh distribution. Complete the method rayleigh(double x, int sigma) that returns the value of y...
Consider the following cumulative distribution function for X. 7 0.1 08 0.9 1.0 Fo) 0.3 0.6 (i) Determine the probability distribution. ii) Find P(X < 1). iii Find P(0 <XS5).