# Question: Let X1 Xn be independent and identically

Let X1, . . . ,Xn be independent and identically distributed random variables. Find

E[X1|X1 + · · · + Xn = x]

E[X1|X1 + · · · + Xn = x]

**View Solution:**## Answer to relevant Questions

Prove Proposition 2.1 when (a) X and Y have a joint probability mass function; (b) X and Y have a joint probability density function and g(x, y) ≥ 0 for all x, y. Let X be a random variable having finite expectation μ and variance σ2, and let g(∙) be a twice differentiable function. Show that Expand g(∙) in a Taylor series about μ. Use the first three terms and ignore the ...A certain component is critical to the operation of an electrical system and must be replaced immediately upon failure. If the mean lifetime of this type of component is 100 hours and its standard deviation is 30 hours, how ...Fifty numbers are rounded off to the nearest integer and then summed. If the individual roundoff errors are uniformly distributed over (−.5, .5), approximate the probability that the resultant sum differs from the exact ...Customers arrive at a bank at a Poisson rate λ. Suppose that two customers arrived during the first hour. What is the probability that (a) Both arrived during the first 20 minutes? (b) At least one arrived during the first ...Post your question