Quiz about Z-transform

Question 1

Z transforms of unit step function is

Accepted Answer

$$\frac{z}{z-1}$$

Answer

$$\frac{z}{z-a}$$

Answer

1

Answer

0

Question 2

Which of the following is damping rule?

Accepted Answer

$$Z\left\{a^nf\left(n\right)\right\}=F\left(\frac{z}{a}\right)$$

Answer

$$\left\{z\left(nf\left(z\right)\right)\right\}=-Z\ \frac{d}{dz}F\left(z\right)$$

Answer

$$Z\left\{f(n-k)\right\}=z^{-n}F\left(z\right)$$

Answer

$$Z\left\{f\left(n+1\right)\right\}=zF\left(z\right)-zf\left(0\right)$$

Question 3

Find the Z - transform of $$f\left(k\right)=c^k\sin\alpha k,\ \ \ k\ge0$$

Accepted Answer

$$\frac{cz\sin\alpha}{z^2-2cz\cos\alpha+c^2}\ ,\ \ z>c$$

Answer

$$\frac{cz\sin\alpha}{z^2+2cz\cos\alpha+c^2}\ ,\ \ z>c$$

Answer

$$\frac{cz\sin\alpha}{z^2-2cz\cos\alpha+c^2}\ ,\ \ z

Answer

$$\frac{cz\sin\alpha}{z^2-2cz\cos\alpha+c^2}\ ,\ \ z\ge c$$

Question 4

$$Z\left\{k\right\}=$$

Accepted Answer

$$\frac{z}{\left(z-1\right)^2}$$

Answer

$$\frac{1}{z-1}$$

Answer

$$\frac{z}{z+1}$$

Answer

$$\frac{z}{z-1}$$

Question 5

Solve $$Z\ \left\{\frac{1}{5^k}\cdot\frac{1}{7^k}\right\}=$$

Accepted Answer

$$\left(\frac{5z}{5z-1}\right)\left(\frac{7z}{7z-1}\right)\ ,\ \left|z\right|>\frac{1}{5}$$

Answer

$$\left(\frac{z}{z-5}\right)\left(\frac{z}{z-7}\right)\ ,\ \left|z\right|>7$$

Answer

$$\left(\frac{5z}{5z-1}\right)\left(\frac{7z}{7z-1}\right)\ ,\ \left|z\right|>\frac{1}{7}$$

Answer

$$\left(\frac{5z}{5z-1}\right)\left(\frac{7z}{7z-1}\right)\ ,\ \left|z\right|\ge\frac{1}{5}$$

Question 6

Solve inverse Z transform of $$F\left(z\right)=\frac{z}{\left(z-1\right)\left(z-2\right)}\ ,\left|z\right|>2$$

Accepted Answer

$$2^k-1\ \ \ ,\ k\ge1$$

Answer

$$2^k+1\ \ \ ,\ k\ge1$$

Answer

$$2^k+1\ \ \ ,\ k>1$$

Answer

$$2^k-1\ \ \ ,\ k>1$$

Question 7

A random Sample of 50 items gives the gives the mean 6.2 and variance 10.24 . can it be regarded as drawn from a normal population with mean 5.4 at 5% level of Significance?

Accepted Answer

NH Accepted ,the sample is drawn from the population with mean 5.4

Answer

AH Accepted ,the sample is drawn from the population with mean 5.4

Answer

NH Accepted ,the sample is drawn from the population with mean 6.2

Answer

AH Accepted ,the sample is drawn from the population with mean 6.2

Question 8

Sample size n is taken to be small if

Accepted Answer

$$n<30$$

Answer

$$n\ge30$$

Answer

$$n\le30$$

Answer

$$n>30$$

Question 9

We use the 't' variable when

Accepted Answer

When the number of samples is small

Answer

The 'z' variable cannot be found

Answer

When the number of samples is large

Answer

When we know the value of the population mean

Question 10

The mean height of random Sample of 100 individuals from a polpulation is 160 . the S.D. of the sample is 10.would it be reasonable to suppose that the mean height of the population is 165 ?

Accepted Answer

$$\left|Z\right|=5$$

Answer

$$\left|Z\right|=-5$$

Answer

$$\left|Z\right|=3$$

Answer

$$\left|Z\right|=1.96$$

Z-transform

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