A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump withtwo hoses. Let x denote the number of hoses being used on the self-service island at a particular time, and let y denote the

number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying

tabulation.

y

p(x,y)

0

1

2

0

0.10

0.03

0.02

1

0.06

0.20

0.08

2

0.05

0.14

0.32

(a) What is P(X = 1 and Y = 1)?

P(X = 1 and Y = 1) = 2

(b) Compute P(X S 1 and Y S 1).

PIX S1 and Y < 1) = 39
(c) Give a word description of the event {X = 0 and Y + 0}.
One hose is in use on one island.
At most one hose is in use at both islands.
One hose is in use on both islands.
At least one hose is in use at both islands.
Compute the probability of this event.
P(X + 0 and Y = 0) = .74
(d) Compute the marginal pmf of X.
0
1
2
Px(x) .15
34
.51
Compute the marginal pmf of Y.
y
0
1
2
Pylv) 21
37
42
Using Py(x), what is P(X < 1)?
P(X S 1) = .49
A certain market has both an express checkout line and a superexpress checkout line. Let X, denote the number of
customers in line at the express checkout at a particular time of day, and let X, denote the number of customers in line at
the superexpress checkout at the same time. Suppose the joint pmf of X, and X2 is as given in the accompanying table.
X₂
0
1
2
3
0
0.09
0.07
0.04
0.00
1
0.05
0.15
0.05
0.04
X1
2
0.05
0.04
0.10
0.06
3
0.00
0.04
0.04
0.07
0.05
4
0.00
0.01
0.05
=
(a) What is P(X2 = 1, X2 = 1), that is, the probability that there is exactly one customer in each line?
P(X1 = 1, X2 = 1) = .15
=
=
(b) What is P(X2 = x2), that is, the probability that the numbers of customers in the two lines are identical?
P(X1 = x2) = .41
=
(c) Let A denote the event that there are at least two more customers in one line than in the other line. Express A in
terms of X1 and X2:
O A = {X1 52 + X2 UX2 5 2 + X1}
O A = {x1 2 2 + X20X2 2 + X1}
O A = {X1 2 2 + X2 UX2 2 2 + x;}
O A = {X1 5 2 + X2 UX2 2 2 + X1}
22+
+
+
+
Calculate the probability of this event.
P(A) = 23
=
(d) What is the probability that the total number of customers in the two lines is exactly four? At least four?
P(exactly four) .18
Plat least four) = .46
Lecture 1 - Introduction and Overview.pdf
Lecture 2 - Events and Counting Outcomes.pdf
Lecture 3 - Probabilistic Models.pdf
Lecture 4 - Conditional Probability and Independence.pdf
Lecture 5 - Bayesian Theorem and Examples.pdf
Lecture 6 - Discrete Random Variables.pdf
Lecture 7 - Statistical Mean and Variance.pdf
Lecture 8 - Some Distributions of Discrete Random Variables.pdf
Lecture 9 - Continuous Random Variables.pdf

Lecture 10 – Statistical Mean and Variance of Continuous RVs

Lecture 11 – Some Distributions of Continuous Random Variables.pdf

Lecture 12 – Transformation of a Random Variable.pdf

Lecture 13 – Joint Distribution of Two Discrete RVs.pdf

Lecture 14 – Joint Distribution of Two Continuous RVS

Lecture 15 – Conditional Probability and Independence

Hardware Engineeri…

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ir

Question 1

In the following circuit, we want to find i(t) for t>0:

182

w w

www

t=07

1 Ω

gov

+

1 F

2

$ 1H

NI

(a) The steady-state value of i(t) is:

(b) The type of response i(t)

(c) The coefficients of the characteristics equations are s? + Xs +Y = 0, where X:

and Y:

(d) Final solution for i(t) is

No new data to save. Last checked at 8:01am

OLG

Question 2

9 p

For the following circuit, the coupling coefficient k=1.

K1

0.5

pr

K

th

ad

100 Cosat

to

14

(但

The mutual inductance is

The phasor current passing through coil 1 is

and coil 2 is

The real power delivered by the voltage source is

and reactive power delivered

IS

. Here the power factor is

Previous

Next >

Not saved

Submit

CS

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The total points are 27, where 2 bonus points are distributed.

9 pts

Question 3

a) Find the transfer function in standard form using

V.(w)

I(W)

b) Zero(s) are @

and pole(s) are at

c) Sketch the Bode plot for magnitude and phase. (The value of H at w=1 is

d) What type of filter can be presented by this transfer function

icLt)

I

R

10

31

Vol

LG

lalu

Assign

XC

х

Submit Answer

time left…

1:14:35

(-/3 Points]

DETAILS

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Let X denote the voltage at the output of a microphone, and suppose that X has a uniform distribution on the interval from –1 to 1. The voltage is processed by a “hard limiter” with cutoff values –0.5 and 0.5, so the limiter output is a random variable Y related to X by

Y = X if |X] S 0.5, Y = 0.5 if X > 0.5, and Y = -0.5 if x < -0.5.
(a) What is P(Y = 0.5)?
(b) Obtain the cumulative distribution function of y.
y

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