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IITM BS Week 4 Statistics 2 Questions | Prasnya
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12Q
01
The probability density function of a random variable
X
X
X
is given as:
f
X
(
x
)
=
{
0.2
,
0
≤
x
<
1
,
c
x
,
1
≤
x
<
2
,
0.4
,
2
≤
x
<
3
,
0
,
otherwise.
f_X(x) = \begin{cases} 0.2, & 0 \le x < 1, \\ cx, & 1 \le x < 2, \\ 0.4, & 2 \le x < 3, \\ 0, & \text{otherwise.} \end{cases}
f
X
(
x
)
=
⎩
⎨
⎧
0.2
,
c
x
,
0.4
,
0
,
0
≤
x
<
1
,
1
≤
x
<
2
,
2
≤
x
<
3
,
otherwise.
Find the value of
c
c
c
.
Single correct
EASY
3 marks
10 May 2026
02
If
X
∼
Exp
(
λ
)
X \sim \text{Exp}(\lambda)
X
∼
Exp
(
λ
)
, then find the PDF of
Y
=
X
Y = \sqrt{X}
Y
=
X
.
Single correct
MEDIUM
3 marks
13 April 2025
03
Find the value of
k
k
k
.
Comprehension
EASY
1 marks
13 April 2025
04
Calculate the value of
F
X
(
0.5
)
F_X(0.5)
F
X
(
0.5
)
.
Comprehension
EASY
2 marks
13 April 2025
05
What is the value of
P
(
0.2
<
X
<
0.5
)
P(0.2 < X < 0.5)
P
(
0.2
<
X
<
0.5
)
? Enter the answer correct to three decimal places.
Comprehension
MEDIUM
2 marks
13 April 2025
06
If
P
(
X
≤
k
)
=
0.95
P(X \le k) = 0.95
P
(
X
≤
k
)
=
0.95
, then find the value of
k
k
k
.
Comprehension
MEDIUM
3 marks
28 April 2024
07
Find the value of
P
(
10
≤
X
≤
15
)
P(10 \le X \le 15)
P
(
10
≤
X
≤
15
)
.
Comprehension
EASY
2 marks
28 April 2024
08
What is the probability that a randomly selected light bulb will last more than 150 hours?
Comprehension
EASY
2 marks
24 December 2023
09
Find
P
(
X
>
300
∣
X
>
200
)
P(X > 300 \mid X > 200)
P
(
X
>
300
∣
X
>
200
)
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
24 December 2023
10
Find the value of
k
k
k
. Enter the answer correct to one decimal place.
Comprehension
EASY
1 marks
03 September 2023
11
Let
F
X
(
x
)
F_X(x)
F
X
(
x
)
be the CDF of
X
X
X
. Calculate the value of
F
X
(
0.5
)
F_X(0.5)
F
X
(
0.5
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
2 marks
03 September 2023
12
Find the expected value of
X
X
X
.
Comprehension
MEDIUM
2 marks
03 September 2023
Showing 12 questions.
Complete question index for this section:
Question 1 (single):
Question 2 (single):
Question 3 (comprehension):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (comprehension):
Question 10 (comprehension):
Question 11 (comprehension):
Question 12 (comprehension):
