# Question: Use the conditional variance formula to determine the variance of

Use the conditional variance formula to determine the variance of a geometric random variable X having parameter p.

## Answer to relevant Questions

Let X be a normal random variable with parameters μ = 0 and σ2 = 1, and let I, independent of X, be such that P{I = 1} = 1/2 = P{I = 0}. Now define Y by In words, Y is equally likely to equal either X or −X. (a) Are X ...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 ...Let X1, . . . ,X20 be independent Poisson random variables with mean 1. (a) Use the Markov inequality to obtain a bound on (b) Use the central limit theorem to approximate Let Zn, n ≥ 1, be a sequence of random variables and c a constant such that, for each ε > 0, P{|Zn − c| > ε}→0 as n→∞. Show that, for any bounded continuous function g, E[g(Zn)]→g(c) as n→∞ Explain how you could use random numbers to approximate ∫10 k(x) dx, where k(x) is an arbitrary function. If U is uniform on (0, 1), what is E[k(U)]?Post your question