1A.Based on an analysis of sample data, an article proposed the pdf f(x) = 0.25e−0.25(x −...

1A.Based on an analysis of sample data, an article proposed the pdf

f(x) = 0.25e^{−0.25(x −
1)} when x ≥ 1as a model for the distribution of X = time (sec) spent at the median line. (Round your answers to three decimal places.)

(a) What is the probability that waiting time is at most 2 sec? More than 2 sec?

at most 2 sec		P(X ≤ 2)	=
more than 2 sec		P(X > 2)	=

(b) What is the probability that waiting time is between 6 and 7 sec?

2B.

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) =

x < 0

x²

0 ≤ x < 4

4 ≤ x

Use the cdf to obtain the following. (If necessary, round your answer to four decimal places.)

(a) Calculate P(X ≤ 3).

(b) Calculate P(2.5 ≤ X ≤ 3).

(c) Calculate P(X > 3.5).

(d) What is the median checkout duration ? [solve 0.5 = F()].

(e) Obtain the density function f(x).
f(x) = F '(x) =

(f) Calculate E(X).

(g) Calculate V(X) and σ_x.

Solutions

Expert Solution

orchestra answered 1 year ago

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