# Question: A filling station is supplied with gasoline once a week

A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function

what must the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is .01?

what must the capacity of the tank be so that the probability of the supply’s being exhausted in a given week is .01?

## Answer to relevant Questions

Compute E[X] if X has a density function given by (a) (b) (c) Let Z be a standard normal random variable Z, and let g be a differentiable function with derivative g′. (a) Show that E[g′(Z)] = E[Zg(Z)] (b) Show that E[Zn+1] = nE[Zn−1] (c) Find E[Z4]. Show that Make the change of variables y = √2x and then relate the resulting expression to the normal distribution. Let X be a random variable that takes on values between 0 and c. That is, P{0 ≤ X ≤ c} = 1. Show that Var(X) ≤ c2/4 One approach is to first argue that E[X2] ≤ cE[X] and then use this inequality to show that Var(X) ...The joint density of X and Y is given by (a) Are X and Y independent? If, instead, f (x, y) were given by (b) Would X and Y be independent?Post your question