Show by defining appropriate random variables

Q: Show by defining appropriate random variablesProve that(a) .transtutors.com/qimage/image02042015246.png” alt=””> and in general,(b) .transtutors.com/qimage/image02042015247.png” alt=””>Show by defining appropriate random variables .transtutors.com/qimage/image02042015248.png” alt=””> and by taking expectations in part (b) how to obtain the well-known formula .transtutors.com/qimage/image02042015249.png” alt=””>(c) Consider n independent Poisson processes—the ith having rate ?i. Derive an expression for the expected time until an event has occurred in all n processes