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IITM BS Week 2 Statistics 2 Questions | Prasnya
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15Q
01
The joint probability mass function of two discrete random variables
X
X
X
and
Y
Y
Y
is given by
f
X
Y
(
x
,
y
)
=
{
x
y
36
,
x
,
y
∈
{
1
,
2
,
3
}
,
0
,
otherwise.
f_{XY}(x,y)=\begin{cases}\dfrac{xy}{36}, & x,y\in\{1,2,3\},\\ 0, & \text{otherwise.}\end{cases}
f
X
Y
(
x
,
y
)
=
{
36
x
y
,
0
,
x
,
y
∈
{
1
,
2
,
3
}
,
otherwise.
What is the value of
P
(
X
+
Y
=
4
)
P(X+Y=4)
P
(
X
+
Y
=
4
)
? Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
06 April 2026
02
Let
X
X
X
be a discrete random variable with PMF as follows. Suppose
X
1
,
X
2
∼
X_1, X_2 \sim
X
1
,
X
2
∼
i.i.d.
X
X
X
. Define
Y
=
X
1
+
X
2
Y=X_1+X_2
Y
=
X
1
+
X
2
. Which of the following option(s) is/are true about the moment generating function of
Y
Y
Y
?
Multiple correct
MEDIUM
3 marks
03 August 2025
03
Let
X
∼
U
n
i
f
o
r
m
{
1
,
2
}
X\sim\mathrm{Uniform}\{1,2\}
X
∼
Uniform
{
1
,
2
}
be discrete. Let
(
Y
∣
X
=
1
)
∼
E
x
p
(
1
)
(Y\mid X=1)\sim\mathrm{Exp}(1)
(
Y
∣
X
=
1
)
∼
Exp
(
1
)
and
(
Y
∣
X
=
2
)
∼
E
x
p
(
2
)
(Y\mid X=2)\sim\mathrm{Exp}(2)
(
Y
∣
X
=
2
)
∼
Exp
(
2
)
. Find the distribution of
Y
Y
Y
.
Single correct
MEDIUM
3 marks
16 March 2025
04
The joint PMF table of two discrete random variables
X
1
X_1
X
1
and
X
2
X_2
X
2
is given. Which option(s) is/are true?
Multiple correct
MEDIUM
3 marks
16 March 2025
05
Calculate
F
Z
(
3
)
F_Z(3)
F
Z
(
3
)
. Enter the answer correct to two decimal places.
Comprehension
EASY
4 marks
16 March 2025
06
Find the range of
Z
Z
Z
.
Comprehension
EASY
1 marks
01 December 2024
07
Find
P
(
Z
=
3
)
P(Z=3)
P
(
Z
=
3
)
.
Comprehension
EASY
2 marks
01 December 2024
08
Which of the following option(s) is/are true? The joint PMF table of two discrete random variables
X
1
X_1
X
1
and
X
2
X_2
X
2
is given as:
Multiple correct
MEDIUM
3 marks
24 March 2024
09
Let
X
,
Y
,
Z
∼
i.i.d. Geometric
(
1
/
2
)
X, Y, Z \sim \text{i.i.d. Geometric}(1/2)
X
,
Y
,
Z
∼
i.i.d. Geometric
(
1/2
)
. Define a new random variable
U
=
min
(
X
,
Y
,
Z
)
U = \min(X, Y, Z)
U
=
min
(
X
,
Y
,
Z
)
. What is the value of
1
/
P
(
U
≥
3
)
1/P(U \ge 3)
1/
P
(
U
≥
3
)
?
Numerical
MEDIUM
3 marks
06 August 2023
10
Suppose
X
∼
Bernoulli
(
0.4
)
X \sim \text{Bernoulli}(0.4)
X
∼
Bernoulli
(
0.4
)
and
Y
∣
X
=
x
∼
Uniform
(
x
−
1
,
x
+
1
)
Y\mid X=x \sim \text{Uniform}(x-1,x+1)
Y
∣
X
=
x
∼
Uniform
(
x
−
1
,
x
+
1
)
. Find the density of
Y
Y
Y
.
Single correct
MEDIUM
3 marks
06 August 2023
11
Let
(
X
,
Y
)
∼
Uniform
(
D
)
(X,Y)\sim \text{Uniform}(D)
(
X
,
Y
)
∼
Uniform
(
D
)
. Which of the following may represent a region
D
D
D
such that
X
X
X
and
Y
Y
Y
are independent?
Single correct
MEDIUM
3 marks
06 August 2023
12
Find the range of
Z
Z
Z
.
Comprehension
EASY
1 marks
02 April 2023
13
Find the value of
P
(
0
<
Z
<
3
)
P(0<Z<3)
P
(
0
<
Z
<
3
)
.
Comprehension
MEDIUM
2 marks
02 April 2023
14
Find the range of
Z
Z
Z
.
Comprehension
EASY
1 marks
20 November 2022
15
Find the probability mass function (PMF) of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
20 November 2022
Showing 15 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (multiple):
Question 3 (single):
Question 4 (multiple):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (multiple):
Question 9 (integer):
Question 10 (single):
Question 11 (single):
Question 12 (comprehension):
Question 13 (comprehension):
Question 14 (comprehension):
Question 15 (comprehension):
