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The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = {0.075x + (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 1 0.07 0.075x + 0.2 dx = 0.2 (b) Calculate P(X ≤ 4). 2 3 ≤x≤ 5 otherwise 3 2 3 = 1.9375 - 4 5 4 5 5 X X f(x) 0.6 0.5 Verify that the total area under the density curve is indeed 1. 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = {0.075x + (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 1 0.07 0.075x + 0.2 dx = 0.2 (b) Calculate P(X ≤ 4). 2 3 ≤x≤ 5 otherwise 3 2 3 = 1.9375 - 4 5 4 5 5 X X f(x) 0.6 0.5 Verify that the total area under the density curve is indeed 1. 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X

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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Please solve a, b, and c.

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. Jo.075x + 0.2 (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 f(x) 0.6 0.5 0.4 0.3 f(x) 0.2 0.1 5 1 1 0.075x + 0.2 dx = 2 (b) Calculate P(X ≤ 4). 2 3 ≤ x ≤ 5 otherwise = 1.9375 3 3 4 5 3 4 5 X Verify that the total area under the density curve is indeed 1. X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 X
Transcribed Image Text:The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. Jo.075x + 0.2 (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 f(x) 0.6 0.5 0.4 0.3 f(x) 0.2 0.1 5 1 1 0.075x + 0.2 dx = 2 (b) Calculate P(X ≤ 4). 2 3 ≤ x ≤ 5 otherwise = 1.9375 3 3 4 5 3 4 5 X Verify that the total area under the density curve is indeed 1. X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 1 2 3 4 5 X
(b) Calculate P(X ≤ 4). How does this probability compare to P(X < 4)? O P(X ≤ 4) < P(X < 4) P(X ≤ 4) > P(X < 4) P(X ≤ 4) = P(X < 4) (c) Calculate P(3.5 ≤ X ≤ 4.5). Calculate P(4.5 < X).
Transcribed Image Text:(b) Calculate P(X ≤ 4). How does this probability compare to P(X < 4)? O P(X ≤ 4) < P(X < 4) P(X ≤ 4) > P(X < 4) P(X ≤ 4) = P(X < 4) (c) Calculate P(3.5 ≤ X ≤ 4.5). Calculate P(4.5 < X).
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