A grocery store has n watermelons to sell and makes $1.00 on each sale. Say the number of consumers of these watermelons is a random variable with a distribution that can be approximated by
A pdf of the continuous type. If the grocer does not have enough watermelons to sell to all consumers, she figures that she loses $5.00 in goodwill from each unhappy customer. But if she has surplus watermelons, she loses 50 cents on each extra watermelon. What should n be to maximize profit?
Answer to relevant QuestionsFor each of the following functions, (i) Find the constant c so that f(x) is a pdf of a random variable X, (ii) Find the cdf, F(x) = P(X ≤ x), (iii) Sketch graphs of the pdf f(x) and the distribution function F(x), and ...Telephone calls arrive at a doctor’s office according to a Poisson process on the average of two every 3 minutes. Let X denote the waiting time until the first call that arrives after 10 a.m. (a) What is the pdf of X? (b) ...If X is N(μ, σ2), show that the distribution of Y = aX + b is N(aμ + b, a2σ2), a ≠ 0. The weekly gravel demand X (in tons) follows the Pdf However, the owner of the gravel pit can produce at most only 4 tons of gravel per week. Compute the expected value of the tons sold per week by the owner. Find the mean and variance of X if the cdf of X is
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