Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container

This video explains the solution of following question:

Let X denote the amount of space occupied by an article placed in a 1-ft3 packing container. The pdf of X is below:

f(x)= 90*x^8* (1-x), x is between 0 and 1
0 ,otherwise

(a) Graph the pdf.
Find the cdf and graph the cdf.
(b) What is P(X is less than equal to 0.65) [i.e. F(0.65)]?
(Round your answer to four decimal places.)
(c) Using the cdf from(a), what is P(X is greater than 0.40 and less than equal to 0.65)?
(Round your answer to four decimal places.)
What is P(X is greater than equal to 0.40 and less than equal to 0.65)?
(Round your answer to four decimal places.)
(d)What is the 75th percentile of the distribution?
(Round your answer to four decimal places.)
(e) Compute E(X) and σ_X.
(Round your answer to four decimal places.)
(f) What is the probability that is more than 1 standard
deviation from its mean value?
(Round your answer to four decimal places.)

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-------Content of this video---------
This video has 18 pages. Page 1 and 2 has question. Page 3 to Page 17 consists of solution and last page is the end screen. Following are the time stamps::

0:00 Question (page 1)
0:10 Question (page 2)
0:21 Solution (page 3-Drawing pdf)
0:33 Solution (page 4-Drawing pdf continue)
0:44 Solution (page 5-Drawing pdf continue)
0:55 Solution (page 6-Finding CDF)
1:07 Solution (page 7-Drawing CDF)
1:18 Solution (page 8-Drawing CDF-continue)
1:29 Solution (page 9-part b)
1:41 Solution (page 10-part c)
1:52 Solution (page 11-part c continue)
2:03 Solution (page 12-part d)
2:15 Solution (page 13-part e)
2:26 Solution (page 14-part e continue)
2:37 Solution (page 15-part e continue)
2:49 Solution (page 16-part f)
3:00 Solution (page 17-part f continue)
3:11 End

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#sackoffruit #jointpdf #covariance #correlation #correlationcoefficient