# components working at a particular time

#### oyth94

##### Member
Hello .Sorry for all the questions I am asking....but I have another one I would like to seek help for.:

Suppose a system has 10 components and that a particular time the jth component is working with probability 1/j for j= 1,2,...10. How many components do you expect to be working at that particular time?

All I have done so far is calculating the probability for all 10 components and I know that the sum of all possible probabilities is 1.

But how should I solve the question?

#### chisigma

##### Well-known member
Hello .Sorry for all the questions I am asking....but I have another one I would like to seek help for.:

Suppose a system has 10 components and that a particular time the jth component is working with probability 1/j for j= 1,2,...10. How many components do you expect to be working at that particular time?

All I have done so far is calculating the probability for all 10 components and I know that the sum of all possible probabilities is 1.

But how should I solve the question?
The expected number of working components is...

$\displaystyle E\{n\} = 1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{10} = H_{10}\ (1)$

Since the status of components are independent r.v. nothing can be said about the sum of their probabilities...

Kind regards

$\chi$ $\sigma$