Question

# Really need help with this question as soon as possible.

A component of a computer

has an active life, measured in discrete units, that is a random variable T where

P(T =1)=0.4, P(T=2)=0.6.

Suppose one starts with a fresh component and each component is replaced by a new component

upon failure.

Define a Markov chain Xn, n=0, 1, . . ., by letting Xn be the age of the component in service at time n. The lifetimes of consecutive components are independently distributed. We also take the convention that Xn=0 at the time of failure. The state space of Xn is {0, 1}.

As an example, if the first component works for 2 periods and the second component works for 1 periods, then we have

X0 =0, X1 =1, X2 =0, X3 =0, ....

(1). Determine the long run probability that a failure occurs in a single period.

Hint: this is related to the limiting distribution of Xn.

(2). What is the expected time between failures?

### Recently Asked Questions

- Which ones of the following arecontinuousrandom variables?(Note: you have to tickallcorrect options) Select one or more: a.Number of customers in a queue

- A survey of23 retirees was taken. Among other things, the retirees were asked to report the age at which they retired. Here are those23 ages (in years). 33,

- What is the 84th percentile of a z distribution? Hint: Find b, such that P(Z < b) = 0.84