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IITM BS Week 1 Statistics 2 Questions | Prasnya
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14Q
01
If
E
[
X
]
=
3
E[X] = 3
E
[
X
]
=
3
, then find the value of
x
4
x_4
x
4
.
Comprehension
MEDIUM
3 marks
10 May 2026
02
Find the value of
λ
\lambda
λ
for which
4
P
(
X
=
2
)
=
5
P
(
X
=
1
)
4 P(X = 2) = 5 P(X = 1)
4
P
(
X
=
2
)
=
5
P
(
X
=
1
)
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
10 May 2026
03
Find
E
[
X
2
]
E[X^2]
E
[
X
2
]
. Enter the answer correct to two decimal places.
Comprehension
EASY
3 marks
10 May 2026
04
If
E
[
X
]
=
4
E[X] = 4
E
[
X
]
=
4
, then what will be the value of
x
3
x_3
x
3
?
Comprehension
MEDIUM
1 marks
13 April 2025
05
Find the value of
Var
(
X
)
\text{Var}(X)
Var
(
X
)
.
Comprehension
MEDIUM
2 marks
13 April 2025
06
Find the value of
P
(
X
=
1
or
X
=
2
)
P(X = 1 \text{ or } X = 2)
P
(
X
=
1
or
X
=
2
)
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
28 April 2024
07
What is the value of
P
(
1
2
<
X
<
5
2
|
X
>
1
)
P\left( \frac{1}{2} < X < \frac{5}{2} \;\middle|\; X > 1 \right)
P
(
2
1
<
X
<
2
5
X
>
1
)
? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
28 April 2024
08
A random variable
X
X
X
has the following probability mass function: If
E
(
X
)
=
2
E(X) = 2
E
(
X
)
=
2
, then what will be the value of
x
3
x_3
x
3
?
Numerical
EASY
3 marks
24 December 2023
09
Sushant first throws a fair die, then throws as many fair coins as the number that showed on the die. If the die showed 5, then find the conditional probability that 3 heads are obtained. Enter the answer correct to three decimal places.
Numerical
MEDIUM
3 marks
30 April 2023
10
Find the value of
p
p
p
for which
9
P
(
X
=
4
)
=
P
(
X
=
2
)
9P(X = 4) = P(X = 2)
9
P
(
X
=
4
)
=
P
(
X
=
2
)
.
Comprehension
MEDIUM
2 marks
30 April 2023
11
Find
E
[
X
2
]
E[X^2]
E
[
X
2
]
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
30 April 2023
12
The joint PMF of two discrete random variables
X
X
X
and
Y
Y
Y
is given by
f
X
Y
(
x
,
y
)
=
x
y
3
,
for
x
=
0
,
1
,
2
;
y
=
0
,
1
f_{XY}(x,y) = \frac{xy}{3}, \quad \text{for } x = 0, 1, 2; y = 0, 1
f
X
Y
(
x
,
y
)
=
3
x
y
,
for
x
=
0
,
1
,
2
;
y
=
0
,
1
Find
P
(
0
<
X
≤
1
∣
Y
=
1
)
P(0 < X \le 1 \mid Y = 1)
P
(
0
<
X
≤
1
∣
Y
=
1
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
11 December 2022
13
Choose the correct option(s) from the following (
T
X
TX
T
X
refers to the values taken by a random variable
X
X
X
):
Comprehension
MEDIUM
2 marks
07 August 2022
14
Calculate
P
(
X
1
=
0
,
X
2
=
1
∣
X
3
=
1
)
P(X_1 = 0, X_2 = 1 \mid X_3 = 1)
P
(
X
1
=
0
,
X
2
=
1
∣
X
3
=
1
)
. Note: Enter the answer correct to one decimal place.
Comprehension
EASY
1 marks
07 August 2022
Showing 14 questions.
Complete question index for this section:
Question 1 (comprehension):
Question 2 (comprehension):
Question 3 (comprehension):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (integer):
Question 9 (integer):
Question 10 (comprehension):
Question 11 (comprehension):
Question 12 (integer):
Question 13 (comprehension):
Question 14 (comprehension):
