Mathematics, 31.03.2020 16:38 yoyoho6218
A gas station sells two grades of gasoline: regular and super. These are priced at $2.00 and $3.00 per gallon, respectively. Let X₁ and X₂ denote the amounts of these grades purchased (gallons) on a particular day. Suppose X₁ and X₂ are independent Normal random variables with E(X₁) = 1000, sd(X₁) = 90, E(X₂) = 800, and sd(X₂) = 45. The revenue from sales is Y = 2X₁ + 3X₂. (a) Find the mean and standard deviation of Y, i. e., E(Y) and sd(Y). (b) Find the probability that the revenue Y does not exceed 4500. Hint: Y is Normally distributed. (c) Find the probability that the gas station sells regular gasoline more, i. e., pr (X₁ > X₂). Attach the R codes or write out the formula(s) you used for full credit.
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A gas station sells two grades of gasoline: regular and super. These are priced at $2.00 and $3.00 p...
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