For numbers 25-27, consider the following. The amount of gold X (in ounces) that a prospec-tor digs in a a day is a random variable with the following pdf:fx(x) = 6x(1 – x)I(0,1)(x)Assuming that the price of gold Y (in dollars) per ounce is uniformly distributed over theinterval [1700, 2000] and is independent of X. Answer the following questions.25. Are X and Y independent?26. What is the expected amount of gold a prospector digs in a day?"27. What is the expected earnings in a day?

25) It is given that X is independent of Y The amount of gold digs and the price of gold are…

Answered: 25. Are X and Y independent? 26. What…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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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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25. Are X and Y independent? 26. What is the expected amount of gold a prospector digs in a day? 27. What is the expected earnings in a day?