### Problem 2: Gas Station Daily SalesConsider a gas station’s daily sales. Let \( Y \) be the volume of gas sold per day in **1000s of gallons**. Assume the distribution of \( Y \) follows this probability density function (pdf):\[f(y) = \begin{cases} k \left( y - \frac{1}{y^3} \right) & \text{for } 1 \leq y \leq 2 \\ 0 & \text{elsewhere}\end{cases}\]#### Questions:a. **What value of \( k \) is required for the above function to be a valid pdf?**b. **Verify that the function given is a valid probability density function.**c. **Determine the cumulative distribution function (cdf) of the random variable.**d. **Compute the probability that there is exactly 1500 gallons of sales on a given day.** (Hint: Find \( P(Y = 1.5) \))

Answered: Image /qna-images/answer/e1d54587-3ac0-4df5-9544-9f9c17647711.jpg

Answered: 2. Consider a gas station's daily…

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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