11/19/21, 12:52 PM UTS CLO 2: Attempt review

TEORI PELUANG IF-44-08 [IPL]

Dashboard / My courses / CII2G3-IF-44-08 / UTS / UTS CLO 2

Started on Monday, 8 November 2021, 2:57 PM

State Finished

Completed on Monday, 8 November 2021, 3:31 PM

Time taken 33 mins 48 secs

Marks 3.67/16.00

Grade 22.92 out of 100.00

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 1/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 1

Complete

Mark 0.17 out of 1.00

[ID] Diberikan fungsi massa peluang gabungan (joint pmf) dari bivariat X,Y. Manakah pernyataan yang benar.

[EN] Given joint probability mass function of X and Y . Which ones are true.
⎧⎪
⎪⎪ x+y
⎪ ; x = 0,1,2, dan y = 0,1,2
p X,Y (x,y) = ⎪⎨⎪⎪ 18
⎪⎪
⎪⎩ 0 ; x,y la innya

Select one or more:

4
E (X) =
3

 5
E (XY) =
3

 8
E (X) =
3

 1
Cov (X,Y) = −
9

5
Cov (X,Y) =
3

The correct answers are:

4 5
E (X) = , E (XY) = ,
3 3
1
Cov (X,Y) = −
9

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 2/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 2

Complete

Mark 0.17 out of 1.00

[ID] Sebuah restaurant memberlakukan fasilitas drivethrough dan dine-in terbatas. Pada hari yang terpilih secara acak,
misalkan X dan Y berturut-turut adalah proporsi waktu drive-through dan dine-in terbatas digunakan, dan misalkan fpp
bersama X dan Y adalah sebagai berikut. 

[EN] A restaurant runs facilities for limited drive-through and dine-in. Suppose X and Y are time proportion for drive-through
and dine-in respectively, with joint probability distribution as follow. 

2
(x + 2y), 0 ≤ x ≤ 1, 0 ≤ y ≤ 1
3
f (x, y) = {
0, x, y lainnya

Select one or more:

X dan Y tidak saling bebas (X and Y are dependent)

 fungsi marjinal Y dari fpp f(x,y) (the marginal probability function of Y ):

∞ 1
2 2 1
h(y) = ∫ f (x, y)dx = ∫ (x + 2y)dx = ( + 2y)
−∞ 0
3 3 2

fungsi marjinal X dari fpp f(x,y) (the marginal probability function of X ):

∞ 1
2 2
2
g(x) = ∫ f (x, y)dy = ∫ (x + 2y)dy = x
−∞ 0
3 3

 fungsi marjinal Y dari fpp f(x,y) (the marginal probability function of Y ):

∞ 1
2 2
h(y) = ∫ f (x, y)dx = ∫ (x + 2y)dx = 2y
−∞ 0
3 3

 fungsi marjinal X dari fpp f(x,y) (the marginal probability function of X ):

∞ 1
2 2
g(x) = ∫ f (x, y)dy = ∫ (x + 2y)dy = (x + 1)
−∞ 0
3 3

The correct answers are: fungsi marjinal X dari fpp f(x,y) (the marginal probability function of X ):

∞ 1
2 2
g(x) = ∫ f (x, y)dy = ∫ (x + 2y)dy = (x + 1)
−∞ 0
3 3

., fungsi marjinal Y dari fpp f(x,y) (the marginal probability function of Y ):

∞ 1
2 2 1
h(y) = ∫ f (x, y)dx = ∫ (x + 2y)dx = ( + 2y)
−∞ 0
3 3 2

., X dan Y tidak saling bebas (X and Y are dependent)

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 3/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 3

Complete

Mark 0.00 out of 1.00

[ID] Diketahui fungsi padat peluang dari peubah acak kontinu X. Manakah pernyataan yang benar.

[EN] Given the probability density function of continuous random variable X . Which the following are true.

Select one or more:

 a.

b.

 c.

 d.

e.

The correct answers are:

,

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 4/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 4

Complete

Mark -0.25 out of 1.00

[ID] Sebuah toko

menjual obral 15 radio, diantara radio tersebut terdapat 5 radio yang rusak. Jika seorang calon
pembeli
melakukan test terhadap 3 radio yang dipilih secara acak, maka ……

Catatan : peubah acak X = jumlah radio yang rusak

[EN] A store gives 15 radio sales including five damaged radios. Suppose X is the number of damaged radios. If someone picks
three radios randomly then ... 

Select one:

115
E (X ) =
91

E (3X − 1) = 3

E (X ) = ∑ x p (x)

E (X ) = ∫ x f (x) dx
0 ≤ E (X ) ≤ 1

The correct answer is: E (X ) = ∑ x p (x)

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 5/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 5

Complete

Mark 0.67 out of 1.00

[ID] Sebuah toko

menjual obral 15 radio, diantara radio tersebut terdapat 5 radio yang rusak. Jika seorang calon
pembeli
melakukan test terhadap 3 radio yang dipilih secara acak, maka ……

Catatan : peubah acak X = jumlah radio yang rusak

[EN] A store gives 15 radio sales including five damaged radios. Suppose X is the number of damaged radios. If someone picks
three radios randomly then ...

Select one or more:

 P(1 < X < 3) = F(2) - F(0)

 P(1 < X < 3) = 5/7

P(X < 3) = 1 - P(X > 3)

P(X > 1) = 1 - P(X < 1)

 P(X = 3) = 1 - F(3)

The correct answers are:

P(1 < X < 3) = F(2) - F(0),

P(1 < X < 3) = 5/7

Question 6

Complete

Mark 1.00 out of 1.00

[ID] Jika X dan Y adalah sembarang peubah acak dengan fungsi peluang bersama f(x,y) dan a, b, dan c adalah koefisien konstan,
maka untuk Z = aX + bY + c

[EN] If two random variables X and Y with joint probability function f(x, y), then for a, b, c are constant values and Z = aX + bY + c

2
Var(Z) = σ Z = a 2 Var(X) + b 2 Var(Y)

Select one:
True

False

The correct answer is 'True'.

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 6/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 7

Complete

Mark 0.00 out of 1.00

[ID] Diketahui
X adalah variabel random dengan fungsi distribusi :

[EN] Given the probability function of discrete random variable \( X \):

x 0 1 2 3 4
F(x) 0.41 0.78 0.94 0.99 1.00

Select one or more:

Var (X − 1) = 0,8456

Var (2X − 1) = E (X 2) − [E (X )]2

 Var (2X − 5) = − 0 . 6516


E ( X 2 − 4) = ∑ ( X 2 − 4) F (x)

E (3X 2 − 4X + 1) = 9,38

The correct answers are: E (3X 2 − 4X + 1) = 9,38 ,

Var (X − 1) = 0,8456

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 7/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 8

Complete

Mark 0.17 out of 1.00

[ID] X merupakan peubah acak kontinyu. Diketahui bahwa \(E(X)

= 2\) dan \(E[X(X-4)] = 5\). Pilihlah pernyataan berikut yang
benar.

[EN] Suppose \( X \) is continuous random variable. Given that \( E(X) = 2 \) and \( E(X(X-4)) = 2 \). Which the following are true.

Select one or more:

A.
\[E[X^2] = 13\]

 B. \[Var(X) = 9\]

C.
\[Var(-4X
+ 12) = 16\cdot Var(X) = 48\]

 D.
\[Var(X) = 3\]

E.
\[E[X^2] = 7\]

The correct answers are:

\[E[X^2] = 13\]
, \[Var(X) = 9\]

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 8/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 9

Complete

Mark 0.00 out of 1.00

[ID] Sebuah toko buku mengeluarkan 8 buku baru pada

bulan ini, yang terdiri dari 3 novel, 2 komik, dan 3 buku resep masakan.
Seseorang membeli 3 buah buku di toko tersebut hari ini. Jika X dan Y
masing-masing menyatakan jumlah Novel dan Komik yang dia
beli, maka pernyataan yang betul adalah :

[EN] A particular store releases eight new books on this month which are three novels, two comics and three cookbooks. This day,
someone buy three books at the store. Suppose \( X \) and \( Y \) are the number of novels and comics that he intends to buy.
Which the following are true?

Select one or more:

1
p X,Y (0,0) = p X,Y (3,0) =
56

 X dan Y saling independen (\( X \) and \( Y \) are independent)

 fungsi massa peluang marjinal untuk X (the marginal probability of \( X \)):

fungsi massa peluang marjinal untuk X (the marginal probability of \( X \))

fungsi massa peluang marjinal untuk Y (the marginal probability of \( Y \))

The correct answers are:

1
p X,Y (0,0) = p X,Y (3,0) = ,
56
fungsi massa peluang marjinal untuk X (the marginal probability of \( X \)):

fungsi massa peluang marjinal untuk Y (the marginal probability of \( Y \))

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 9/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 10

Complete

Mark 0.17 out of 1.00

[ID] Probability density function (pdf) dari suatu variable random X diketahui sebagai berikut:
[EN] Given the probability density function of random variable \( X \)

Jika E[X]=0.2, tentukan mana dari pernyataan-pernyataan berikut ini yang benar.
If \( E(X)=0.2 \), which the following are true.

Select one or more:

A.
\[a = 1 \text{ dan } b=\frac{1}{2}\].

 B.
\[a = 2,8 \text{ dan } b=-3,6\].

C. \[E(X^2) = 0.033\]

 D.
\[Var(-4X
+ 12) = 16\cdot Var(X) = 4,28\]

E.
\[a = 1 \text{ dan } b=0\].

The correct answers are:

\[a = 2,8 \text{ dan } b=-3,6\].
, \[E(X^2) = 0.033\]

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 10/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 11

Complete

Mark 0.00 out of 1.00

[ID] Diketahui fungsi padat peluang dari peubah acak kontinu X. Manakah pernyataan yang benar.

[EN] Given the probability density function of continuous random variable \( X \). Which the following are true.

Select one or more:

 a.

b.

 c.

 d.

e.

The correct answers are:

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 11/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 12

Complete

Mark 0.17 out of 1.00

[ID] Diberikan fungsi massa peluang gabungan (joint pmf) dari bivariat X,Y. Manakah pernyataan yang betul 

[EN] Given the joint probability mass function of \( X \) and \( Y \). Which ones are true.

Select one or more:

fungsi massa peluang marjinal untuk X (the marginal probability function of \( X \)):

 X dan Y saling bebas (\( X \) and \( Y \) are independent)

 9
k=
56

18
k=
56

 fungsi massa peluang marjinal untuk Y (the marginal probability function of \( Y \)):

The correct answers are:

9
k= ,
56
fungsi massa peluang marjinal untuk X (the marginal probability function of \( X \)):

fungsi massa peluang marjinal untuk Y (the marginal probability function of \( Y \)):

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 12/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 13

Complete

Mark -0.25 out of 1.00

[ID] Fungsi
peluang dari suatu peubah acak diskret X dinyatakan sebagai berikut :
[EN} Given the probability function of discrete random variable \( X \):
⎧⎪
⎪⎪
⎪⎪ 2p ; x =1
⎪⎪ p ; x =2
P (X = x) = ⎪⎨⎪⎪
⎪⎪ 4p ; x =3
⎪⎪
⎪⎪
⎩ 0 ; x lainnya

Select one:

P (X > 1) = F (2) −F (1)

1
p=
7

p =7

P (X ≤ 1) = 1 −P (X = 1)

2
P (X = 3) =
7

The correct answer is:

1
p=
7

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 13/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 14

Complete

Mark 0.67 out of 1.00

[ID] Di dalam tas berisi 5 bola yang ukurannya sama, dengan komposisi  2 bola warna merah, 2 bola warna kuning , dan 1 bola
warna putih. Selanjutnya dipilih 3 bola secara acak. Misalkan X adalah peubah acak yang menyatakan banyaknya bola warna
merah yang terpilih, dan peubah acak Y menyatakan banyaknya bola warna putih yang terpilih., maka pernyataan yang betul
adalah :

[EN] Five balls in a bag have same size but various colors which are two red, two yellow, and one white. The three balls will be
chosen randomly. Suppose \( X \) is the number of red balls chosen, and \( Y \) presents the number of white balls chosen.
Which the following are true.

Select one or more:

3
Cov (X,Y) = −
25

 6
Var (Y) =
25

 9
Var (X) =
25

3
Cov (X,Y) =
5

3
E (X) =
5

The correct answers are:

9 6
Var (X) = , Var (Y) = ,
25 25
3
Cov (X,Y) = −
25

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 14/15
11/19/21, 12:52 PM UTS CLO 2: Attempt review

Question 15

Complete

Mark 1.00 out of 1.00

[ID] Jika variabel acak X  dan Y  saling bebas dengan h (y) >0  distribusi marjinal terhadap Y  dari  f (x,y) , maka peluang
bersyarat dari X  diberikan  Y = y :

f (x,y)
f (x | y) =
h (y)
tidak lain merupakan distribusi marjinal g (x)  dari fungsi distribusi f (x,y) .

[EN] If the random variable \( X\) and \( Y\) are independent and \( h(y)>0\) is marginal probability function of \( Y\), then the
conditional probability of \( X\) given \( Y=y\) or \[ f(x|y)=\frac{f(x,y)}{h(y)}\]is the marginal probability function of \( X\) or \
(g(x)\).

Select one:
True

False

The correct answer is 'True'.

Question 16

Complete

Mark 0.00 out of 1.00

[ID] Hitunglah nilai kovariansi dari peubah acak kontinyu X dan Y, jika diketahui nilai-nilai:

[EN] Determine the covariance between continuous random variables \( X\) and \( Y\), given

\[\begin{cases} E[X] = \frac{1}{3}, \\ E[Y] = \frac{2}{3}, \\ E[XY] = \frac{1}{4}.\end{cases}\].

ctt: Jawab dengan bil. desimal, lakukan pembulatan 2 angka di belakang koma.  Contoh penulisan jawaban X,XX

Put the answer on decimal number with two number after the semicolon. Example: X,XX

Answer: 0.67

The correct answer is: 0.03

Previous Activity

Jump to...

https://lms.telkomuniversity.ac.id/mod/quiz/review.php?attempt=3321349&cmid=1659279 15/15