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.
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.
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.
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:(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
Transcribed Image Text:Let X denote the amount of space occupied by an article placed in a 1-ft³ packing container. The pdf of X is below.
(56x6 (1-x) 0 < x < 1
0
otherwise
f(x) =
(a) Graph the pdf.
f(x)
4
3
f(x)
4
Obtain the cdf of X.
0.2
F(x) =
0.2
0.4
0
0.4
0.6
+8
0.6
x < 0
0≤x≤ 1
0.8
LL
2
X
0.8
1.0
x > 1
1.0
X
f(x)
4
3
2
f(x)
0.2
0.4
0.2
0.6
0.4
0.8
0.6
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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