Answer:
Explanation:
That is correct. The total life of the n identical components is a random variable and can be expressed as the sum of the lifetimes of each component, that is:
t = x1 + x2 + ... + xn
where x1, x2, ..., xn are identically and independently distributed exponential random variables with the same mean of 10.
The expected value of each component's lifetime is given by E(x) = 1/λ, where λ is the rate parameter of the exponential distribution. Since the expected value of x is 10, we have:
E(x) = 1/λ = 10
=> λ = 1/10
Thus, each component's lifetime follows an exponential distribution with rate parameter λ = 1/10.
The expected value of the total life t is then given by:
E(t) = E(x1 + x2 + ... + xn)
= E(x1) + E(x2) + ... + E(xn) (by linearity of expectation)
= n * E(x)
= n * (1/λ)
= 10n
Therefore, the expected value of the total life of the n identical components is 10n.