MHB Components working at a particular time

[oyth94]

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]

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 $\chi$ $\sigma$