Let X ∼ Exp(λ) with pdf f(x|λ) = λe−λx and λ ∼ Gamma(a, b) with PDF f(λ) = 1 λa−1e−λ/b where a > 0 is the shape parameter and b > 0 is the scale parameter. That Γ(a)ba is to say, the Poisson parameter λ is no longer a constant number; it is a gamma random variable. Find the marginal distribution of X, i. e., write the PDF of X as a function of a and b. (Note that this marginal distribution is called Lomax distribution.)

The a/p clerk of a company writes the checks for vendors, and the controller signs the checks. the a/p clerk hasdevised a plan to give herself a raise. she creates a new vendor for her friend's business and creates two purchaseorders for random car detailing services for $75 and $70. she writes the checks to pay these new vendors knowing thecontroller will only pay close attention to checks over $100. she delivers the checks to her friend to deposit in his bankaccount, and then he writes her a personal check for the full amount of $145.ceventually, what will be the effect of her actions? what can the company do to prevent this type of behavior? due mondav