11. What is the numerator of D[z], if you use the 'class...

11. What is the numerator of D[z], if you use the 'class default' pole/zero mapping discrete equivalent technique to obtain a D[z] given the following D[s]? Let the sample period be T = 0.02 seconds. D[s] = \frac{(2s + 8)}{(s + 1)(s + 2)} (a) K(z - 0.923) (b) K(z - 0.923)(z + 1) (c) K(z - 0.852) (d) K(z - 0.852)(z + 1)

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Transcript

00:01 We have been given a probability density function.

00:04 F of x is equal to 0 .04 for all x between 53 and 78.

00:13 So what kind of distribution are we looking at here? well we're looking at a uniform distribution.

00:20 So if i mark x and f of x on the axes, between 53 and 78, every possible outcome is equally likely to occur.

00:31 So it looks like a box.

00:33 Outside the interval it drops immediately to 0.

00:36 So f of x is 0 otherwise.

00:40 For part a, we want the proportion equivalent to the probability of a random test meeting this criteria, the proportion that require more than 70 seconds.

00:52 So i'll mark that on here.

00:56 So we're looking at this bit here.

00:58 Now this is a probability curve.

01:00 The area of the blue rectangle is 1.

01:02 And if i find the area of the red rectangle, i'll have my solution.

01:06 So i'm going to make a fraction comparing the size of these two rectangles.

01:10 So blue one is 1, or length times height.

01:13 The red is also length times height.

01:16 They have the same height here.

01:17 The height is actually 0 .04.

01:20 So all that is left is to compare the relative lengths of the intervals...

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