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Electronics and Electrical
,
Digital Communication
,
Mathematics
Engineering Mathematics A Foundation for Electronic, Electrical, Communications and Systems Engineers
673 SOLVED PROBLEMS
Question: 29.8
A random variable, y, has a known probability distribution given by y 2 4 6 8 10 P(y) 0.17 0.23 0.2 0.3 0.1 Find the expected value of y. ...
Verified Answer:
We have μ = expected value = 2(0.17) + 4(0.23) + 6...
Question: 29.22
A random variable, h, has a normal distribution with mean 7 and standard deviation 2. Calculate the probability that (a) h > 9 (b) h < 6 (c) 5 < h < 8 ...
Verified Answer:
(a) Applying the transformation gives
9\to{...
Question: 27.19
A cube of side 2 units is constructed with five solid faces and one open face. It is located in the region defined by 0 ≤ x ≤ 2, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2 and its open face is its top face, bounded by the curve C, lying in the plane z = 2, as shown in Figure 27.26. Throughout this region a vector field ...
Verified Answer:
(a) The open face is highlighted in Figure 27.26. ...
Question: 22.32
Find the sequence whose z transform is F(z) = 2z²-z/(z-5)(z+4) ...
Verified Answer:
The first stage is to divide the expression for F(...
Question: 27.18
Consider a solid object such as that shown in Figure 27.17. The density, ρ, of this object may vary from point to point. ...
Verified Answer:
So, at any point P with coordinates (x, y, z), the...
Question: 24.9
Amplitude modulation ...
Verified Answer:
Amplitude modulation is a technique that allows au...
Question: 1.17
Convert 14 397 to a hexadecimal number. ...
Verified Answer:
From Table 1.3 the highest number that does not ex...
Question: 23.22
Consider the circuit of Figure 23.27. Using Kirchhoffs voltage law and Ohm’s law we obtain vi = i R + v0 ...
Verified Answer:
For the capacitor,
v_{\mathrm{o}}=\frac{i}{...
Question: 21.36
There are many examples of position control systems in engineering, for example control of the position of a plotter pen, and control of the position of a radio telescope. The common term for these systems is servo-systems. Consider the block diagram of Figure 21.16 which represents a simple servo-system. ...
Verified Answer:
Consider the block diagram of Figure 21.16 which r...
Question: 12.2
Use the second-derivative test to find all maximum and minimum points of the functions in Example 12.1. ...
Verified Answer:
(a) Given y = x² then y' = 2x and y" = 2. We locat...
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