(ELEC2600)[2012](s)midterm~wpwong^_28356.pdf

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ELEC 2600 Probability and Random Processes in Engineering

2012 Spring Semester - Midterm Exam Paper with Marking Scheme March 16, 2012

SECTION I: Multiple Choice [20 Marks]

1. [4] Which of the following statements is wrong? ( B )

A. The sub-experiments in a sequential experiment can be either dependent or independent;

B. A uniform random variable has flat PDF, so its variance will be 0;

C.

D.

The Binomial distribution describes the number of successes in several independent trails;

and .

Poisson distribution is an approximation to the Binomial distribution with large.

small

.

2.

[4] We perform n independent sequential experiments. In each experiment, therere three

the Whats..

..

.1...

. .

, and .

.....,.

...

.. B, and C. Also, outcomes A, ,.

.. times ( occurs a times and B occurs b.

experiments, nprobability that, among the

..

.

.

.!)?

.!.!

( D )

.

.

.;

A.

.

...! .!

...!

.

.;

.! .!

....

.

.

!

.

B.

.

.

.

.1.

.

.

.

.

.....

..!......!.

.

.

.!.!

.

.

..

!.!.!.!

..

C.

;

.1.....

..!.....

.

.....

.

D.

.

[4] We want to measure the distance from the redbird to the seafront cafeteria. For each

0..follows Gaussian distribution with .

error

0.1|.

|. What is the probability that .9

.

.. .

,....

(Hint:

3.

measurement, the

.

and variance

.

mean

?

( A)

.. ..

...

.

.

). .

.

.

......

......

.

.

.

.

A. 2.....;

.

2 2

B.

..

...;

.

1.2

..

...

C.

;

D. 1.2......

.

1

4. [4] Suppose we roll a fair dice (each digit occurs with equal probability) and we want to get a six. Whats the probability that it will take 4 more trials until we finally get a six for the first time, given that we have already thrown it for 2 times and get two non-six digits? ( C )

A. .......;

B. .......;

C. .......;

D. ........

,.0.4...

.... .

[4] In an experiment, one of the three events follows exponential distribution given .

. Random variable.0.5 ...

. .

, and .0.1 ...

,.5.76 ..VAR,.3.24 ..|.

.VARhappens.).1,2,3 .

... Whatis.0.36 .|.

..

.

2.052;

.

,

.

and

.

occurs. Also

5.

..

VAR

.

.

.|.

.

(

.

.

Besides,

.

and

?

( B )

A.

B. 1.26;

C. 2.1;

D. 1.10.

SECTION II: Problems [80 Marks]

1.

[20 Marks]

find the following probability. ,.0.6... .

,.0.7 ..

..

..0.9...

.. .

(a)If ;....

..[4] Compute ..

..

..[4] Compute ....

..[4] Compute ..

..

..[4] Compute (iv)

| .

, compute.0.56 .|. .

(b)[4] If

...

..

. .

,.0.7 ..

....

.......

.3.

.;.

.

(i)

(ii);

.

(iii);

.

.

.

.

.

.

.

Solution:

.

(a)Because ..

.

and .0.6 ...

.....

...

.

..0.9,.3...0.7.0.6.0.9.0.4.1.

.

(i)

;

.

....

....

.

.

.

..

.

...

..0.6.0.4.0.2.1..

.

(ii)

;

.

....

....

.

.

...

.

.

...

.3...0.7.0.