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Problems 717
★ B–4 A die is tossed. The probability of getting any face is where x = k = 1, 2, 3, 4, 5, or 6.
Find the probability of getting an odd-numbered face.
★ B–5 For the die toss of Prob. B–4, find the probability of getting a 4 when an even-numbered face is
obtained on a toss.
P(x) = 1 6 ,
B–6 Which of the following functions satisfy the properties for a PDF. Why?
(a) f(x) = 1 p a 1
1 + x 2 b
ƒ xƒ , ƒ xƒ 6 1
(b) f(x) = e
0, x otherwise
1
6 (8 - x), 4 … x … 10
(c) f(x) = e
0, x otherwise
3
k=0
q
(d) f(x) = a 4 A1 4 B k d1xk2
B–7 Show that all cumulative distribution functions must satisfy the properties given in Sec. B–5.
B–8 Let f(x) = Ke -b|x| , where K and b are positive constants. Find the mathematical expression for the
CDF and sketch the results.
★ B–9 Find the probability that - 1 4 A … y 1 … 1 4 A for the triangular distribution shown in Fig. B–14b.
B–10 A triangular PDF is shown in Fig. B–14b.
(a) Find a mathematical expression that describes the CDF.
(b) Sketch the CDF.
B–11 Evaluate the PDFs for the two waveforms shown in Fig. PB–11.
A
0.2T 0.8T
A
t
0.7T 0.3T
A
A
t
Figure PB–11