elianagilbert3p3hh63
05.07.2020 •
Mathematics
Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. F(x) = 0 x < 0 x^2/16 0 ≤ x < 4 1 4 ≤ x Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)Required:a. Calculate P(x<=1)b. Calculate P(0.5<= x<=1)c. Calculate P(x>1.5)d. What is the media checkout duration μ? e. Obtain the density function f(x)f. Calculate E(X).
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Ответ:
a) P(x≤1) = 0.0625
b) P(0.5≤x≤1) = 0.0468
c) P(x>1.5) = 0.8593
d) Median (m) = 3.4641
e) f(x) = 0 x < 0
x/8 0≤x≤4
0 x≥4
Step-by-step explanation:
a) To calculate the probability of F(x) with x being less or equal 1 is:
P(x≤1) = F(1)
F(1) =
P(x≤1) = 0.0625
b) To calculate probability of F(x) with x being between 0.5 and 1:
P(0.5≤x≤1) = F(x≤1) - F(x≤0.5) = F(1) - F(0.5)
F(1) = 0.0625
F(0.5) = = 0.0156
P(0.5≤x≤1) = 0.0625 - 0.0156
P(0.5≤x≤1) = 0.0468
c) P(x>1.5) = 1 - P(x≤1.5) = 1 - F(1.5)
F(1.5) = 0.1406
P(x>1.5) = 1 - 0.1406
P(x>1.5) = 0.8593
d) Median is a point in the graph that divides it in half, so to determine the point, here called m:
m³ = 24
m = 3.4641
The median checkout duration is 3.4641 hours.
e) Density function of a cumulative distribution function (cdf) as well as in a continuous random variable is the first derivative of a function. Then, for this function it is:
f(x) = F'(x)
f(x) = 0 x<0
0≤x≤4
0 x≥4
f) E(X) =
=
=
=
=
E(X) = 2.6667
Ответ:
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Step-by-step explanation:
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