2.A retailer for a petroleum product sells a random amount X each day. Suppose that X,measured in thousands of gallons, has the probability density functionf(x)√³x² 0≤x≤2{*{200otherwise=1The retailer's profit turns out to be $100 for each 1000 gallons sold (10 cents per gallon) if X ≤ 1 and$40 extra per 1000 gallons (an extra 4 of cents per gallon) if X > 1. Find the retailer's expected profitfor any given day.

Given a retailer for a petroleum product sells a random amount X each day. Suppose that X, measured…

Answered: 2. A retailer for a petroleum product…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.
4. Sixteen-ounce boxes of shredded wheat cereal packed automatically by machine are sometimes over- weight and sometimes underweight. The actual weight in ounces over or under 16 is a random variable X whose probability density is f(x) = c(4- x²) for -2 < x < 2, and 0 elsewhere. Negative values pertain to ounces under 16. Determine the constant c, and then find the probability that a box of cereal will be (a) more than one ounce underweight.
For a randomly selected county in the United States, let X represent the proportion of adults over age 65 who are employed, or the elderly employment rate. Then, X isrestricted to a value between zero and one. Suppose that the cumulative distribution function(CDF) for X is given by F(x) = 3x^2-2x^3 for 0<=x<=1Find the probability that the elderly employment rate is at least 0.6 (60%).What is the probability that the elderly employment rate is at most 0.3 (30%) course: Applied Statistics and Econometrics
Need help with B and C.
Suppose a random variable X has a probability density function in img.jpg. a. Find the value of k that makes this a probability density function. b. Find P(0.4≤X≤1). c. Find P(X≤0.4|X≤0.8) d. Find F(b) = P(X≤b) and sketch the graph of this function.

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