A continuous random variable X that can assume values between x = 1 and x = 4 has a density function given by f(x) = (a) Show that the area under the curve is equal to 1. (b) Find P(3
A continuous random variable X that can assume values between x = 1 and x = 4 has a density function given by f(x) = (a) Show that the area under the curve is equal to 1. (b) Find P(3
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...
Related questions
Question
Transcribed Image Text:A continuous random variable \( X \) that can assume values between \( x=1 \) and \( x=4 \) has a density function given by \( f(x) = \frac{1}{3} \).
(a) **Show that the area under the curve is equal to 1.**
**(b)** Find \( P(3 < X < 3.8) \).
**(c)** Find \( P(X \leq 1.7) \).
(a) **Which of the following definite integrals shows that the area under the given curve is 1?** Select the correct choice below and fill in the answer box to complete your choice.
- **A.** \(\int_1^4 \left(\frac{1}{3}\right) dx = \Box^4_1 = 1\)
- **B.** \(\int_1^1 \left(\frac{1}{3}\right) dx = \Box^1_1 = 1\)
- **C.** \(\int_{-\infty}^\infty \left(\frac{1}{3}\right) dx = \Box^\infty_{-\infty} = 1\)
- **D.** \(\int_3^4 \left(\frac{1}{3}\right) dx = \Box^4_3 = 1\)
**(b)** \( P(3 < X < 3.8) = \Box \) (Simplify your answer.)
**(c)** \( P(X \leq 1.7) = \Box \) (Simplify your answer.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
