A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows.f(x) = kx2 0 ≤ x ≤ 20 otherwiseFind C and F please. (d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)0.8794(e) Compute E(X) and ox. (Round your answers to four decimal places.)E(X)= 0.7778= 0.1313ox=(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)0.1597X Graph the cdf of X.F(x)1.00.80.60.40.2F(x)1.00.80.60.40.20.20.20.40.40.60.60.80.8- X1.01.0XF(x)1.0What is P(0.25 ≤X ≤ 0.6)? (Round your answer to four decimal places.)0.80.60.40.2F(x)1.00.80.60.40.2(b) What is P(X ≤ 0.6) [i.e., F(0.6)]? (Round your answer to four decimal places.)0.10640.20.20.40.4(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.)0.60.60.80.81.01.0XX

Given: f(x) = kx20≤x≤20Otherwise Mean E(X) = 0.7778 Standard deviation σ = 0.1313

Answered: A college professor never finishes his…

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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Question

A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows.

f(x) =

kx²		0 ≤ x ≤ 2
0		otherwise

Find C and F please.

(d) What is the 75th percentile of the distribution? (Round your answer to four decimal places.)
0.8794
(e) Compute E(X) and ox. (Round your answers to four decimal places.)
E(X)= 0.7778
= 0.1313
ox=
(f) What is the probability that X is more than 1 standard deviation from its mean value? (Round your answer to four decimal places.)
0.1597
X

Graph the cdf of X.
F(x)
1.0
0.8
0.6
0.4
0.2
F(x)
1.0
0.8
0.6
0.4
0.2
0.2
0.2
0.4
0.4
0.6
0.6
0.8
0.8
- X
1.0
1.0
X
F(x)
1.0
What is P(0.25 ≤X ≤ 0.6)? (Round your answer to four decimal places.)
0.8
0.6
0.4
0.2
F(x)
1.0
0.8
0.6
0.4
0.2
(b) What is P(X ≤ 0.6) [i.e., F(0.6)]? (Round your answer to four decimal places.)
0.1064
0.2
0.2
0.4
0.4
(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.)
0.6
0.6
0.8
0.8
1.0
1.0
X
X

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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