(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.) What is P(0.25 ≤ x ≤ 0.6)? (Round your answer to four decimal places.)
(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.) What is P(0.25 ≤ x ≤ 0.6)? (Round your answer to four decimal places.)
(c) Using the cdf from (a), what is P(0.25 < X < 0.6)? (Round your answer to four decimal places.) What is P(0.25 ≤ x ≤ 0.6)? (Round your answer to four decimal places.)
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) =
56x6(1 − x)
0 < x < 1
0
otherwise
FIND C AND F PLEASE.
Transcribed Image Text: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
Transcribed Image Text:(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
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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69114cc4-9b87-45c3-b69a-02f5eb08739b%2Fb59734cf-4cfa-4d87-bb7b-05e890f32228%2Flonaql_processed.png&w=3840&q=75)
