Chapter 3: Q4E (page 116)
Suppose that the c.d.f.Fof a random variableXis as sketched in Fig. 3.9. Find each of the following probabilities:


Short Answer
a.0.1.
b.0.1.
c.0.2
d.0
e.0.6
f.0.4
g.0.7
h.0
i.0
j.0
k.0
l.0.2
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Chapter 3: Q4E (page 116)
Suppose that the c.d.f.Fof a random variableXis as sketched in Fig. 3.9. Find each of the following probabilities:


a.0.1.
b.0.1.
c.0.2
d.0
e.0.6
f.0.4
g.0.7
h.0
i.0
j.0
k.0
l.0.2
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Suppose that the p.d.f. of X is as follows:
\(\begin{aligned}f\left( x \right) &= e{}^{ - x},x > 0\\ &= 0,x \le 0\end{aligned}\)
Determine the p.d.f. of \({\bf{Y = }}{{\bf{X}}^{\frac{{\bf{1}}}{{\bf{2}}}}}\)
Suppose that a random variableXhas the uniform distribution on the interval [−2,8]. Find the p.d.f. ofXand the value of Pr(0<X <7).
Suppose that a random variableXhas a discrete distribution
with the following p.f.:
\(f\left( x \right) = \left\{ \begin{array}{l}\frac{c}{{{2^x}}}\;\;for\;x = 0,1,2,...\\0\;\;\;\;otherwise\end{array} \right.\)
Find the value of the constantc.
Question:Suppose that two persons make an appointment to meet between 5 p.m. and 6 p.m. at a certain location, and they agree that neither person will wait more than 10 minutes for the other person. If they arrive independently at random times between 5 p.m. and 6 p.m. what is the probability that they willmeet?
Suppose that a random variable X has the Bernoulli distribution with the parameter p = 0.7. (See Definition 3.1.5.) Sketch the c. d. f. of X.
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