Prasnya
Prasnya
Continue with Google
Week 2 Statistics 2 Questions | Prasnya
Prasnya
Prasnya
Continue with Google
Statistics 2 > Week 2
All PYQs
Topic Wise PYQs
Start Weekly Test
Type:
All
Difficulty:
All
Year:
All
48Q
01
Let
X
X
X
and
Y
Y
Y
be two independent random variables with the following PMFs. Define a new random variable
Z
=
min
(
X
,
Y
)
Z=\min(X,Y)
Z
=
min
(
X
,
Y
)
. Find the value of
P
(
Z
≤
1
)
P(Z\le 1)
P
(
Z
≤
1
)
. Enter the answer correct to one decimal place.
Numerical
MEDIUM
3 marks
26 October 2025
02
Find the value of
f
X
Y
(
1
,
0
)
+
f
X
Y
(
2
,
0
)
f_{XY}(1,0)+f_{XY}(2,0)
f
X
Y
(
1
,
0
)
+
f
X
Y
(
2
,
0
)
.
Comprehension
MEDIUM
3 marks
26 October 2025
03
What is the range of
Y
Y
Y
?
Comprehension
EASY
2 marks
26 October 2025
04
Suppose that on a particular day oven
O
1
O_1
O
1
and
O
2
O_2
O
2
are operated and
O
3
O_3
O
3
is turned off, then find the value of
P
(
Y
=
2
)
P(Y=2)
P
(
Y
=
2
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
26 October 2025
05
Define a new random variable
Z
=
X
1
+
X
2
Z=X_1+X_2
Z
=
X
1
+
X
2
. Find the value of
P
(
Z
=
2
)
P(Z=2)
P
(
Z
=
2
)
.
Comprehension
EASY
2 marks
26 October 2025
06
Let
X
1
,
X
2
X_1,X_2
X
1
,
X
2
and
X
3
X_3
X
3
be three independent and identically distributed Poisson random variables with mean
λ
=
3
\lambda=3
λ
=
3
. Find the probability that exactly one of the
X
i
X_i
X
i
is equal to
0
0
0
, and the other two variables are greater than
1
1
1
.
Single correct
MEDIUM
3 marks
13 July 2025
07
Which of the following expressions correctly represents the event that an arriving patient cannot be treated?
Comprehension
EASY
2 marks
13 July 2025
08
Find the value of
P
(
Z
≤
1
∣
Y
=
3
)
P(Z\le 1\mid Y=3)
P
(
Z
≤
1
∣
Y
=
3
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
13 July 2025
09
Which of the following option(s) is/are correct?
Comprehension
MEDIUM
3 marks
13 July 2025
10
Find the value of
x
x
x
for which the random variables
X
X
X
and
Y
Y
Y
are independent.
Single correct
MEDIUM
3 marks
23 February 2025
11
If
Z
Z
Z
represents the combined total number of customers arriving at both counters during a one-hour interval, then determine the PMF of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
23 February 2025
12
Which of the following option(s) is/are correct?
Comprehension
HARD
2 marks
23 February 2025
13
Find the range of
Z
∣
Y
=
2
Z\mid Y=2
Z
∣
Y
=
2
.
Comprehension
EASY
1 marks
27 October 2024
14
What is the value of
P
(
Z
=
54
,
Y
=
2
)
P(Z=54,Y=2)
P
(
Z
=
54
,
Y
=
2
)
? Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
27 October 2024
15
Define a new random variable
Z
=
max
(
X
1
,
X
2
,
X
3
)
Z=\max(X_1,X_2,X_3)
Z
=
max
(
X
1
,
X
2
,
X
3
)
. Find the value of
P
(
Z
≤
2
)
P(Z\le2)
P
(
Z
≤
2
)
.
Comprehension
MEDIUM
2 marks
27 October 2024
16
If
X
=
4
X=4
X
=
4
, then which of the following options are true?
Comprehension
EASY
3 marks
27 October 2024
17
Find the value of
100
P
(
Y
=
6
)
100P(Y=6)
100
P
(
Y
=
6
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
27 October 2024
18
Consider a random variable
X
X
X
that takes integer values from
1
1
1
to
10
10
10
with equal probability
1
10
\frac{1}{10}
10
1
. Define another random variable
Y
=
X
m
o
d
4
Y=X\bmod 4
Y
=
X
mod
4
. Find the PMF of
Y
Y
Y
.
Single correct
MEDIUM
3 marks
07 July 2024
19
What is the probability that exactly one out of the three random variables takes value greater than
4
4
4
?
Comprehension
MEDIUM
2 marks
07 July 2024
20
Find the probability
P
(
max
(
X
1
,
X
2
,
X
3
)
>
4
)
P(\max(X_1,X_2,X_3)>4)
P
(
max
(
X
1
,
X
2
,
X
3
)
>
4
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
07 July 2024
21
Find the PMF of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
25 February 2024
22
If
X
=
5
X=5
X
=
5
, then which of the following options are true?
Comprehension
EASY
3 marks
25 February 2024
23
Find the value of
P
(
Y
=
1
∣
X
=
5
)
P(Y=1\mid X=5)
P
(
Y
=
1
∣
X
=
5
)
. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
25 February 2024
24
Find the value of
P
(
Z
≤
3
)
P(Z\le3)
P
(
Z
≤
3
)
.
Comprehension
EASY
3 marks
25 February 2024
25
If
P
(
Z
=
4
)
=
a
36
P(Z=4)=\frac{a}{36}
P
(
Z
=
4
)
=
36
a
, what is the value of
a
a
a
?
Comprehension
EASY
2 marks
25 February 2024
26
Find the range of
Z
Z
Z
.
Comprehension
EASY
1 marks
29 October 2023
27
Find the value of
P
(
Z
=
3
)
P(Z=3)
P
(
Z
=
3
)
.
Comprehension
MEDIUM
2 marks
29 October 2023
28
What is the PMF of
X
X
X
?
Comprehension
MEDIUM
2 marks
29 October 2023
29
Find the PMF of
U
U
U
.
Comprehension
MEDIUM
3 marks
29 October 2023
30
Compute the CDF of
X
X
X
,
F
X
(
k
)
F_X(k)
F
X
(
k
)
, where
k
∈
{
1
,
2
,
3
,
4
,
5
,
6
}
k\in\{1,2,3,4,5,6\}
k
∈
{
1
,
2
,
3
,
4
,
5
,
6
}
.
Comprehension
MEDIUM
2 marks
29 October 2023
31
Find
P
(
X
=
4
)
P(X=4)
P
(
X
=
4
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
29 October 2023
32
Find the value of
λ
\lambda
λ
for which
3
P
(
X
=
3
)
=
2
P
(
X
=
2
)
+
4
P
(
X
=
1
)
3P(X=3)=2P(X=2)+4P(X=1)
3
P
(
X
=
3
)
=
2
P
(
X
=
2
)
+
4
P
(
X
=
1
)
.
Comprehension
MEDIUM
3 marks
29 October 2023
33
Find the range of
U
U
U
.
Comprehension
EASY
1 marks
16 July 2023
34
Find the value of
P
(
X
=
4
,
U
=
8
)
P(X=4,U=8)
P
(
X
=
4
,
U
=
8
)
.
Comprehension
EASY
2 marks
16 July 2023
35
Let a random variable
G
G
G
represent the number of girls selected for the committee. Find the range of
G
G
G
.
Comprehension
EASY
2 marks
16 July 2023
36
If
Z
=
5
Z=5
Z
=
5
, then which of the following options are true?
Comprehension
MEDIUM
3 marks
16 July 2023
37
Let
X
X
X
and
Y
Y
Y
be two independent
Bernoulli
(
1
3
)
\operatorname{Bernoulli}\left(\frac{1}{3}\right)
Bernoulli
(
3
1
)
random variables. Define another random variable
Z
=
∣
X
−
Y
∣
Z=|X-Y|
Z
=
∣
X
−
Y
∣
. Find the PMF of
Z
Z
Z
.
Single correct
MEDIUM
3 marks
16 October 2022
38
Are
X
X
X
and
Y
Y
Y
independent?
Comprehension
MEDIUM
1 marks
16 October 2022
39
Compute the CDF of
X
X
X
,
F
X
(
k
)
F_X(k)
F
X
(
k
)
, where
k
∈
{
1
,
2
,
…
,
6
}
k\in\{1,2,\ldots,6\}
k
∈
{
1
,
2
,
…
,
6
}
.
Comprehension
MEDIUM
2 marks
16 October 2022
40
Find
P
(
X
=
3
)
P(X=3)
P
(
X
=
3
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
16 October 2022
41
If Aman is asked two questions during the interview, what is the probability that he will answer only one correctly? Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
16 October 2022
42
Find
P
(
X
=
Y
)
P(X=Y)
P
(
X
=
Y
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
16 October 2022
43
Which of the following options are true?
Multiple correct
MEDIUM
2 marks
05 June 2022
44
Find the value of
P
(
X
=
1
∣
Z
=
5
)
P(X=1\mid Z=5)
P
(
X
=
1
∣
Z
=
5
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
05 June 2022
45
Find the distribution of
S
=
X
+
Y
S = X + Y
S
=
X
+
Y
.
Comprehension
EASY
2 marks
05 June 2022
46
Find the distribution of
Z
1
=
max
(
X
,
Y
)
Z_1 = \max(X,Y)
Z
1
=
max
(
X
,
Y
)
.
Comprehension
EASY
2 marks
05 June 2022
47
Find the distribution of
Z
2
=
min
(
X
,
Y
)
Z_2 = \min(X,Y)
Z
2
=
min
(
X
,
Y
)
.
Comprehension
EASY
2 marks
05 June 2022
48
Which of the following options are true?
Comprehension
MEDIUM
3 marks
05 June 2022
Showing 48 questions.
Statistics 2 > Week 2
All PYQs
Topic Wise PYQs
Start Weekly Test
Type:
All
Difficulty:
All
Year:
All
48Q
01
Let
X
X
X
and
Y
Y
Y
be two independent random variables with the following PMFs. Define a new random variable
Z
=
min
(
X
,
Y
)
Z=\min(X,Y)
Z
=
min
(
X
,
Y
)
. Find the value of
P
(
Z
≤
1
)
P(Z\le 1)
P
(
Z
≤
1
)
. Enter the answer correct to one decimal place.
Numerical
MEDIUM
3 marks
26 October 2025
02
Find the value of
f
X
Y
(
1
,
0
)
+
f
X
Y
(
2
,
0
)
f_{XY}(1,0)+f_{XY}(2,0)
f
X
Y
(
1
,
0
)
+
f
X
Y
(
2
,
0
)
.
Comprehension
MEDIUM
3 marks
26 October 2025
03
What is the range of
Y
Y
Y
?
Comprehension
EASY
2 marks
26 October 2025
04
Suppose that on a particular day oven
O
1
O_1
O
1
and
O
2
O_2
O
2
are operated and
O
3
O_3
O
3
is turned off, then find the value of
P
(
Y
=
2
)
P(Y=2)
P
(
Y
=
2
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
26 October 2025
05
Define a new random variable
Z
=
X
1
+
X
2
Z=X_1+X_2
Z
=
X
1
+
X
2
. Find the value of
P
(
Z
=
2
)
P(Z=2)
P
(
Z
=
2
)
.
Comprehension
EASY
2 marks
26 October 2025
06
Let
X
1
,
X
2
X_1,X_2
X
1
,
X
2
and
X
3
X_3
X
3
be three independent and identically distributed Poisson random variables with mean
λ
=
3
\lambda=3
λ
=
3
. Find the probability that exactly one of the
X
i
X_i
X
i
is equal to
0
0
0
, and the other two variables are greater than
1
1
1
.
Single correct
MEDIUM
3 marks
13 July 2025
07
Which of the following expressions correctly represents the event that an arriving patient cannot be treated?
Comprehension
EASY
2 marks
13 July 2025
08
Find the value of
P
(
Z
≤
1
∣
Y
=
3
)
P(Z\le 1\mid Y=3)
P
(
Z
≤
1
∣
Y
=
3
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
13 July 2025
09
Which of the following option(s) is/are correct?
Comprehension
MEDIUM
3 marks
13 July 2025
10
Find the value of
x
x
x
for which the random variables
X
X
X
and
Y
Y
Y
are independent.
Single correct
MEDIUM
3 marks
23 February 2025
11
If
Z
Z
Z
represents the combined total number of customers arriving at both counters during a one-hour interval, then determine the PMF of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
23 February 2025
12
Which of the following option(s) is/are correct?
Comprehension
HARD
2 marks
23 February 2025
13
Find the range of
Z
∣
Y
=
2
Z\mid Y=2
Z
∣
Y
=
2
.
Comprehension
EASY
1 marks
27 October 2024
14
What is the value of
P
(
Z
=
54
,
Y
=
2
)
P(Z=54,Y=2)
P
(
Z
=
54
,
Y
=
2
)
? Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
27 October 2024
15
Define a new random variable
Z
=
max
(
X
1
,
X
2
,
X
3
)
Z=\max(X_1,X_2,X_3)
Z
=
max
(
X
1
,
X
2
,
X
3
)
. Find the value of
P
(
Z
≤
2
)
P(Z\le2)
P
(
Z
≤
2
)
.
Comprehension
MEDIUM
2 marks
27 October 2024
16
If
X
=
4
X=4
X
=
4
, then which of the following options are true?
Comprehension
EASY
3 marks
27 October 2024
17
Find the value of
100
P
(
Y
=
6
)
100P(Y=6)
100
P
(
Y
=
6
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
27 October 2024
18
Consider a random variable
X
X
X
that takes integer values from
1
1
1
to
10
10
10
with equal probability
1
10
\frac{1}{10}
10
1
. Define another random variable
Y
=
X
m
o
d
4
Y=X\bmod 4
Y
=
X
mod
4
. Find the PMF of
Y
Y
Y
.
Single correct
MEDIUM
3 marks
07 July 2024
19
What is the probability that exactly one out of the three random variables takes value greater than
4
4
4
?
Comprehension
MEDIUM
2 marks
07 July 2024
20
Find the probability
P
(
max
(
X
1
,
X
2
,
X
3
)
>
4
)
P(\max(X_1,X_2,X_3)>4)
P
(
max
(
X
1
,
X
2
,
X
3
)
>
4
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
07 July 2024
21
Find the PMF of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
25 February 2024
22
If
X
=
5
X=5
X
=
5
, then which of the following options are true?
Comprehension
EASY
3 marks
25 February 2024
23
Find the value of
P
(
Y
=
1
∣
X
=
5
)
P(Y=1\mid X=5)
P
(
Y
=
1
∣
X
=
5
)
. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
25 February 2024
24
Find the value of
P
(
Z
≤
3
)
P(Z\le3)
P
(
Z
≤
3
)
.
Comprehension
EASY
3 marks
25 February 2024
25
If
P
(
Z
=
4
)
=
a
36
P(Z=4)=\frac{a}{36}
P
(
Z
=
4
)
=
36
a
, what is the value of
a
a
a
?
Comprehension
EASY
2 marks
25 February 2024
26
Find the range of
Z
Z
Z
.
Comprehension
EASY
1 marks
29 October 2023
27
Find the value of
P
(
Z
=
3
)
P(Z=3)
P
(
Z
=
3
)
.
Comprehension
MEDIUM
2 marks
29 October 2023
28
What is the PMF of
X
X
X
?
Comprehension
MEDIUM
2 marks
29 October 2023
29
Find the PMF of
U
U
U
.
Comprehension
MEDIUM
3 marks
29 October 2023
30
Compute the CDF of
X
X
X
,
F
X
(
k
)
F_X(k)
F
X
(
k
)
, where
k
∈
{
1
,
2
,
3
,
4
,
5
,
6
}
k\in\{1,2,3,4,5,6\}
k
∈
{
1
,
2
,
3
,
4
,
5
,
6
}
.
Comprehension
MEDIUM
2 marks
29 October 2023
31
Find
P
(
X
=
4
)
P(X=4)
P
(
X
=
4
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
29 October 2023
32
Find the value of
λ
\lambda
λ
for which
3
P
(
X
=
3
)
=
2
P
(
X
=
2
)
+
4
P
(
X
=
1
)
3P(X=3)=2P(X=2)+4P(X=1)
3
P
(
X
=
3
)
=
2
P
(
X
=
2
)
+
4
P
(
X
=
1
)
.
Comprehension
MEDIUM
3 marks
29 October 2023
33
Find the range of
U
U
U
.
Comprehension
EASY
1 marks
16 July 2023
34
Find the value of
P
(
X
=
4
,
U
=
8
)
P(X=4,U=8)
P
(
X
=
4
,
U
=
8
)
.
Comprehension
EASY
2 marks
16 July 2023
35
Let a random variable
G
G
G
represent the number of girls selected for the committee. Find the range of
G
G
G
.
Comprehension
EASY
2 marks
16 July 2023
36
If
Z
=
5
Z=5
Z
=
5
, then which of the following options are true?
Comprehension
MEDIUM
3 marks
16 July 2023
37
Let
X
X
X
and
Y
Y
Y
be two independent
Bernoulli
(
1
3
)
\operatorname{Bernoulli}\left(\frac{1}{3}\right)
Bernoulli
(
3
1
)
random variables. Define another random variable
Z
=
∣
X
−
Y
∣
Z=|X-Y|
Z
=
∣
X
−
Y
∣
. Find the PMF of
Z
Z
Z
.
Single correct
MEDIUM
3 marks
16 October 2022
38
Are
X
X
X
and
Y
Y
Y
independent?
Comprehension
MEDIUM
1 marks
16 October 2022
39
Compute the CDF of
X
X
X
,
F
X
(
k
)
F_X(k)
F
X
(
k
)
, where
k
∈
{
1
,
2
,
…
,
6
}
k\in\{1,2,\ldots,6\}
k
∈
{
1
,
2
,
…
,
6
}
.
Comprehension
MEDIUM
2 marks
16 October 2022
40
Find
P
(
X
=
3
)
P(X=3)
P
(
X
=
3
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
16 October 2022
41
If Aman is asked two questions during the interview, what is the probability that he will answer only one correctly? Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
16 October 2022
42
Find
P
(
X
=
Y
)
P(X=Y)
P
(
X
=
Y
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
16 October 2022
43
Which of the following options are true?
Multiple correct
MEDIUM
2 marks
05 June 2022
44
Find the value of
P
(
X
=
1
∣
Z
=
5
)
P(X=1\mid Z=5)
P
(
X
=
1
∣
Z
=
5
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
05 June 2022
45
Find the distribution of
S
=
X
+
Y
S = X + Y
S
=
X
+
Y
.
Comprehension
EASY
2 marks
05 June 2022
46
Find the distribution of
Z
1
=
max
(
X
,
Y
)
Z_1 = \max(X,Y)
Z
1
=
max
(
X
,
Y
)
.
Comprehension
EASY
2 marks
05 June 2022
47
Find the distribution of
Z
2
=
min
(
X
,
Y
)
Z_2 = \min(X,Y)
Z
2
=
min
(
X
,
Y
)
.
Comprehension
EASY
2 marks
05 June 2022
48
Which of the following options are true?
Comprehension
MEDIUM
3 marks
05 June 2022
Showing 48 questions.
