1 f(x) = kr², k constant, -1 0.5. (c) If P(x > c) = 0.6 then what is the value of c?
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![EXERCISES 29.4
(a) If 200 measurements of z are made, how many,
1 f(x) = kr2, k constant, -1 <*< 1. f(x) is a p.d.f.
on average, will be greater than 1?
(a) What is the value of k?
(b) If 50% of measurements are less than k. find k.
(b) Calculate the probability that x > 0.5.
(c) If P(x > c) = 0.6 then what is the value of c?
A p.d.f., h(x), is defined by
2 f(x) is a p.d.f. for the random variable x, which can
vary from 0 to 10. It is illustrated in Figure 29.5. What
is the probability that x lies in [2, 4]?
3
h(x) =
-1<x<1
Calculate
f(x) A
(a) P(0 <x<0.5)
(b) P(-0.3 < xr < 0.7)
(c) P(x| < 0.5)
(d) P(x > 0.5)
(e) P(x < 0.7)
10
(a) Verify that
Figure 29.5
Probability density function for Question 2.
f(t) = ie-it
A p.d.f. is given by
is suitable as a p.d.f.
f(2) = 2e-22
0<z< 0
(b) Calculate P(t > 2) if 2 = 3.
Solutions
(b) 0.6575
(e) 0.9393
1
(a) 1.5
(b) 0.4375
(c) -0.5848
(a) 0.3438
(c) 0.6875
(d) 0.1563
0.28
(b) 2.479 x 10-3
(а) 27
(b) 0.3466](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ba1fb27-542c-467a-ab5e-58ae02ec77f4%2F086a228a-3a90-40ae-aada-7baa2160bdc0%2Fl3nupl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISES 29.4
(a) If 200 measurements of z are made, how many,
1 f(x) = kr2, k constant, -1 <*< 1. f(x) is a p.d.f.
on average, will be greater than 1?
(a) What is the value of k?
(b) If 50% of measurements are less than k. find k.
(b) Calculate the probability that x > 0.5.
(c) If P(x > c) = 0.6 then what is the value of c?
A p.d.f., h(x), is defined by
2 f(x) is a p.d.f. for the random variable x, which can
vary from 0 to 10. It is illustrated in Figure 29.5. What
is the probability that x lies in [2, 4]?
3
h(x) =
-1<x<1
Calculate
f(x) A
(a) P(0 <x<0.5)
(b) P(-0.3 < xr < 0.7)
(c) P(x| < 0.5)
(d) P(x > 0.5)
(e) P(x < 0.7)
10
(a) Verify that
Figure 29.5
Probability density function for Question 2.
f(t) = ie-it
A p.d.f. is given by
is suitable as a p.d.f.
f(2) = 2e-22
0<z< 0
(b) Calculate P(t > 2) if 2 = 3.
Solutions
(b) 0.6575
(e) 0.9393
1
(a) 1.5
(b) 0.4375
(c) -0.5848
(a) 0.3438
(c) 0.6875
(d) 0.1563
0.28
(b) 2.479 x 10-3
(а) 27
(b) 0.3466
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