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Week 4 Statistics 2 Questions | Prasnya
Statistics 2 > Week 4
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Topic-Wise PYQs
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Type:
All
Difficulty:
All
Year:
All
29Q
01
Let
X
∼
Exponential
(
1
)
X\sim \text{Exponential}(1)
X
∼
Exponential
(
1
)
with PDF
f
X
(
x
)
=
e
−
x
f_X(x)=e^{-x}
f
X
(
x
)
=
e
−
x
,
x
>
0
x>0
x
>
0
. Define a random variable
Y
=
3
X
+
1
Y=3X+1
Y
=
3
X
+
1
. Find the value of
f
Y
(
6
)
f_Y(6)
f
Y
(
6
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
06 April 2026
02
Find the value of
k
k
k
.
Comprehension
MEDIUM
2 marks
06 April 2026
03
Find the value of
P
(
X
≤
0.5
)
P(X\le 0.5)
P
(
X
≤
0.5
)
. Enter the answer correct to one decimal place.
Comprehension
MEDIUM
3 marks
06 April 2026
04
If
X
∼
N
o
r
m
a
l
(
1
,
16
)
X \sim \mathrm{Normal}(1,16)
X
∼
Normal
(
1
,
16
)
and
Z
=
(
X
−
1
)
/
4
Z=(X-1)/4
Z
=
(
X
−
1
)
/4
, then find
P
(
X
2
>
16
)
P(X^2>16)
P
(
X
2
>
16
)
.
Single correct
MEDIUM
3 marks
03 August 2025
05
Find the value of
k
k
k
.
Comprehension
EASY
2 marks
03 August 2025
06
Find
P
(
0
≤
X
≤
1
/
2
)
P(0\le X\le1/2)
P
(
0
≤
X
≤
1/2
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
03 August 2025
07
Find
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
16 March 2025
08
Find
Var
(
X
)
\operatorname{Var}(X)
Var
(
X
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
16 March 2025
09
If
X
∼
E
x
p
(
λ
)
X\sim\mathrm{Exp}(\lambda)
X
∼
Exp
(
λ
)
, find the PDF of
Y
=
X
2
Y=X^2
Y
=
X
2
.
Single correct
MEDIUM
3 marks
01 December 2024
10
Find
k
k
k
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
01 December 2024
11
If
E
[
X
]
=
0.7
E[X]=0.7
E
[
X
]
=
0.7
, find
Var
(
X
)
\operatorname{Var}(X)
Var
(
X
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
01 December 2024
12
Let
X
∼
E
x
p
o
n
e
n
t
i
a
l
(
3
)
X\sim\mathrm{Exponential}(3)
X
∼
Exponential
(
3
)
with PDF
f
X
(
x
)
=
3
e
−
3
x
f_X(x)=3e^{-3x}
f
X
(
x
)
=
3
e
−
3
x
,
x
>
0
x>0
x
>
0
. Find the PDF of
Y
=
2
X
+
3
Y=2X+3
Y
=
2
X
+
3
.
Single correct
MEDIUM
3 marks
04 August 2024
13
Find
E
[
Y
]
E[Y]
E
[
Y
]
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
04 August 2024
14
Find the PDF of
Y
Y
Y
.
Comprehension
MEDIUM
2 marks
04 August 2024
15
Let
X
X
X
be a continuous random variable with PDF
f
X
(
x
)
=
4
x
3
f_X(x)=4x^3
f
X
(
x
)
=
4
x
3
for
0
<
x
≤
1
0<x\le 1
0
<
x
≤
1
, and
0
0
0
otherwise. Find the PDF of
Y
=
X
3
Y=X^3
Y
=
X
3
.
Single correct
MEDIUM
3 marks
03 December 2024
16
Find the CDF of
Y
Y
Y
.
Comprehension
MEDIUM
2 marks
03 December 2024
17
Find
P
(
1
≤
Y
≤
6.25
)
P(1\le Y\le 6.25)
P
(
1
≤
Y
≤
6.25
)
. Enter the answer correct to one decimal place.
Comprehension
MEDIUM
2 marks
03 December 2024
18
Find the value of
k
k
k
such that
f
(
x
)
f(x)
f
(
x
)
is a valid PDF. Hint:
∫
e
−
a
x
d
x
=
−
e
−
a
x
/
a
\int e^{-ax}\,dx=-e^{-ax}/a
∫
e
−
a
x
d
x
=
−
e
−
a
x
/
a
.
Comprehension
EASY
2 marks
06 August 2023
19
What is the probability that rainfall in the local area will be at most 10 inches? Enter the answer correct to 3 decimal places.
Comprehension
MEDIUM
3 marks
06 August 2023
20
The probability density function of a continuous random variable
X
X
X
is given by
f
(
x
)
=
6
x
+
1
10
f(x)=\frac{6x+1}{10}
f
(
x
)
=
10
6
x
+
1
for
1
≤
x
≤
2
1\le x\le2
1
≤
x
≤
2
, and
0
0
0
otherwise. Find the value of
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Numerical
EASY
3 marks
02 April 2023
21
Find the value of
k
k
k
.
Comprehension
EASY
2 marks
02 April 2023
22
Find the value of
P
(
0.25
≤
X
≤
0.75
)
P(0.25\le X\le0.75)
P
(
0.25
≤
X
≤
0.75
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
02 April 2023
23
The probability density function of a continuous random variable
X
X
X
is given by
f
(
x
)
=
2
x
f(x)=2x
f
(
x
)
=
2
x
for
0
<
x
<
1
0<x<1
0
<
x
<
1
, and
0
0
0
otherwise. Find the value of
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Numerical
EASY
3 marks
20 November 2022
24
What is the probability that a patient selected at random who went through the treatment will survive for more than
2
2
2
years?
Comprehension
EASY
2 marks
20 November 2022
25
Find
P
(
X
>
6
∣
X
>
4
)
P(X>6\mid X>4)
P
(
X
>
6
∣
X
>
4
)
.
Comprehension
EASY
3 marks
20 November 2022
26
Which among the following represents the cumulative distribution function (CDF) of
X
X
X
?
Comprehension
MEDIUM
2 marks
10 July 2022
27
Find the value of
P
(
X
<
2.5
)
P(X<2.5)
P
(
X
<
2.5
)
. Enter the answer correct to two decimal places.
Comprehension
EASY
1 marks
10 July 2022
28
Find the probability density function of
Y
Y
Y
.
Comprehension
MEDIUM
3 marks
10 July 2022
29
Find the value of
P
(
Y
≥
2
)
P(Y\ge2)
P
(
Y
≥
2
)
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
10 July 2022
Showing 29 questions.
Statistics 2 > Week 4
All PYQs
Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
29Q
01
Let
X
∼
Exponential
(
1
)
X\sim \text{Exponential}(1)
X
∼
Exponential
(
1
)
with PDF
f
X
(
x
)
=
e
−
x
f_X(x)=e^{-x}
f
X
(
x
)
=
e
−
x
,
x
>
0
x>0
x
>
0
. Define a random variable
Y
=
3
X
+
1
Y=3X+1
Y
=
3
X
+
1
. Find the value of
f
Y
(
6
)
f_Y(6)
f
Y
(
6
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
06 April 2026
02
Find the value of
k
k
k
.
Comprehension
MEDIUM
2 marks
06 April 2026
03
Find the value of
P
(
X
≤
0.5
)
P(X\le 0.5)
P
(
X
≤
0.5
)
. Enter the answer correct to one decimal place.
Comprehension
MEDIUM
3 marks
06 April 2026
04
If
X
∼
N
o
r
m
a
l
(
1
,
16
)
X \sim \mathrm{Normal}(1,16)
X
∼
Normal
(
1
,
16
)
and
Z
=
(
X
−
1
)
/
4
Z=(X-1)/4
Z
=
(
X
−
1
)
/4
, then find
P
(
X
2
>
16
)
P(X^2>16)
P
(
X
2
>
16
)
.
Single correct
MEDIUM
3 marks
03 August 2025
05
Find the value of
k
k
k
.
Comprehension
EASY
2 marks
03 August 2025
06
Find
P
(
0
≤
X
≤
1
/
2
)
P(0\le X\le1/2)
P
(
0
≤
X
≤
1/2
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
03 August 2025
07
Find
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
16 March 2025
08
Find
Var
(
X
)
\operatorname{Var}(X)
Var
(
X
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
16 March 2025
09
If
X
∼
E
x
p
(
λ
)
X\sim\mathrm{Exp}(\lambda)
X
∼
Exp
(
λ
)
, find the PDF of
Y
=
X
2
Y=X^2
Y
=
X
2
.
Single correct
MEDIUM
3 marks
01 December 2024
10
Find
k
k
k
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
01 December 2024
11
If
E
[
X
]
=
0.7
E[X]=0.7
E
[
X
]
=
0.7
, find
Var
(
X
)
\operatorname{Var}(X)
Var
(
X
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
01 December 2024
12
Let
X
∼
E
x
p
o
n
e
n
t
i
a
l
(
3
)
X\sim\mathrm{Exponential}(3)
X
∼
Exponential
(
3
)
with PDF
f
X
(
x
)
=
3
e
−
3
x
f_X(x)=3e^{-3x}
f
X
(
x
)
=
3
e
−
3
x
,
x
>
0
x>0
x
>
0
. Find the PDF of
Y
=
2
X
+
3
Y=2X+3
Y
=
2
X
+
3
.
Single correct
MEDIUM
3 marks
04 August 2024
13
Find
E
[
Y
]
E[Y]
E
[
Y
]
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
04 August 2024
14
Find the PDF of
Y
Y
Y
.
Comprehension
MEDIUM
2 marks
04 August 2024
15
Let
X
X
X
be a continuous random variable with PDF
f
X
(
x
)
=
4
x
3
f_X(x)=4x^3
f
X
(
x
)
=
4
x
3
for
0
<
x
≤
1
0<x\le 1
0
<
x
≤
1
, and
0
0
0
otherwise. Find the PDF of
Y
=
X
3
Y=X^3
Y
=
X
3
.
Single correct
MEDIUM
3 marks
03 December 2024
16
Find the CDF of
Y
Y
Y
.
Comprehension
MEDIUM
2 marks
03 December 2024
17
Find
P
(
1
≤
Y
≤
6.25
)
P(1\le Y\le 6.25)
P
(
1
≤
Y
≤
6.25
)
. Enter the answer correct to one decimal place.
Comprehension
MEDIUM
2 marks
03 December 2024
18
Find the value of
k
k
k
such that
f
(
x
)
f(x)
f
(
x
)
is a valid PDF. Hint:
∫
e
−
a
x
d
x
=
−
e
−
a
x
/
a
\int e^{-ax}\,dx=-e^{-ax}/a
∫
e
−
a
x
d
x
=
−
e
−
a
x
/
a
.
Comprehension
EASY
2 marks
06 August 2023
19
What is the probability that rainfall in the local area will be at most 10 inches? Enter the answer correct to 3 decimal places.
Comprehension
MEDIUM
3 marks
06 August 2023
20
The probability density function of a continuous random variable
X
X
X
is given by
f
(
x
)
=
6
x
+
1
10
f(x)=\frac{6x+1}{10}
f
(
x
)
=
10
6
x
+
1
for
1
≤
x
≤
2
1\le x\le2
1
≤
x
≤
2
, and
0
0
0
otherwise. Find the value of
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Numerical
EASY
3 marks
02 April 2023
21
Find the value of
k
k
k
.
Comprehension
EASY
2 marks
02 April 2023
22
Find the value of
P
(
0.25
≤
X
≤
0.75
)
P(0.25\le X\le0.75)
P
(
0.25
≤
X
≤
0.75
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
02 April 2023
23
The probability density function of a continuous random variable
X
X
X
is given by
f
(
x
)
=
2
x
f(x)=2x
f
(
x
)
=
2
x
for
0
<
x
<
1
0<x<1
0
<
x
<
1
, and
0
0
0
otherwise. Find the value of
E
[
X
]
E[X]
E
[
X
]
. Enter the answer correct to two decimal places.
Numerical
EASY
3 marks
20 November 2022
24
What is the probability that a patient selected at random who went through the treatment will survive for more than
2
2
2
years?
Comprehension
EASY
2 marks
20 November 2022
25
Find
P
(
X
>
6
∣
X
>
4
)
P(X>6\mid X>4)
P
(
X
>
6
∣
X
>
4
)
.
Comprehension
EASY
3 marks
20 November 2022
26
Which among the following represents the cumulative distribution function (CDF) of
X
X
X
?
Comprehension
MEDIUM
2 marks
10 July 2022
27
Find the value of
P
(
X
<
2.5
)
P(X<2.5)
P
(
X
<
2.5
)
. Enter the answer correct to two decimal places.
Comprehension
EASY
1 marks
10 July 2022
28
Find the probability density function of
Y
Y
Y
.
Comprehension
MEDIUM
3 marks
10 July 2022
29
Find the value of
P
(
Y
≥
2
)
P(Y\ge2)
P
(
Y
≥
2
)
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
10 July 2022
Showing 29 questions.
