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 by2 f(x) is a p.d.f. for the random variable x, which canvary from 0 to 10. It is illustrated in Figure 29.5. Whatis the probability that x lies in [2, 4]?3h(x) =-1 0.5)(e) P(x < 0.7)10(a) Verify thatFigure 29.5Probability density function for Question 2.f(t) = ie-itA p.d.f. is given byis suitable as a p.d.f.f(2) = 2e-220 2) if 2 = 3.Solutions(b) 0.6575(e) 0.93931(a) 1.5(b) 0.4375(c) -0.5848(a) 0.3438(c) 0.6875(d) 0.15630.28(b) 2.479 x 10-3(а) 27(b) 0.3466

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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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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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