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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)
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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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.)
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.)
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