Answered: The actual tracking weight of a stereo…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.

f(x) =

1 − (x − 3)²

2 ≤ x ≤ 4

otherwise

(a) Sketch the graph of f(x).

(b) Find the value of k.

(c) What is the probability that the actual tracking weight is greater than the prescribed weight?

(d) What is the probability that the actual weight is within 0.2 g of the prescribed weight? (Round your answer to four decimal places.)

(e) What is the probability that the actual weight differs from the prescribed weight by more than 0.4 g? (Round your answer to four decimal places.)

(I only need help with part b through e)

The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.
– 3)2]
— (х —
2 < x5 4
f(x) =
otherwise
(a) Sketch the graph of f(x).
f(x)
f(x)
1.0F
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5
f(x)
f(x)
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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