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IITM BS Week 2 Statistics 2 Questions | Prasnya
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9Q
01
Let
X
X
X
be a discrete random variable with PMF as follows:\nSuppose
X
1
,
X
2
,
X
3
∼
i.i.d.
X
X_1, X_2, X_3 \sim \text{i.i.d. } X
X
1
,
X
2
,
X
3
∼
i.i.d.
X
. Define a new random variable
Y
=
X
1
+
X
2
+
X
3
Y = X_1 + X_2 + X_3
Y
=
X
1
+
X
2
+
X
3
. Which of the following option(s) is (are) true about the moment generating function of the random variable
Y
Y
Y
?
Multiple correct
MEDIUM
3 marks
10 May 2026
02
Define a new random variable
Y
=
X
+
1
Y = X + 1
Y
=
X
+
1
. Find the value of
P
(
1
<
Y
<
4
)
P(1 < Y < 4)
P
(
1
<
Y
<
4
)
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
10 May 2026
03
Find the PMF of
Z
Z
Z
.
Comprehension
MEDIUM
3 marks
22 December 2024
04
Let
X
X
X
and
Y
Y
Y
be two independent Bernoulli(1/3) random variables. Define another random variable
Z
=
∣
Y
−
X
∣
Z = |Y - X|
Z
=
∣
Y
−
X
∣
. Find the expectation of
Z
Z
Z
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
01 September 2024
05
Find
P
(
X
=
5
)
P(X = 5)
P
(
X
=
5
)
. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
01 September 2024
06
Find the expected value of
X
X
X
. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
01 September 2024
07
Let
X
1
,
X
2
,
X
3
∼
i.i.d.
X
X_1, X_2, X_3 \sim \text{i.i.d. } X
X
1
,
X
2
,
X
3
∼
i.i.d.
X
and
X
∼
Uniform
{
−
0.2
,
0.2
}
X \sim \text{Uniform}\{-0.2, 0.2\}
X
∼
Uniform
{
−
0.2
,
0.2
}
. Define a new random variable
S
=
X
1
+
X
2
+
X
3
S = X_1 + X_2 + X_3
S
=
X
1
+
X
2
+
X
3
. Find the MGF (moment generating function) of
S
S
S
.
Single correct
MEDIUM
3 marks
28 April 2024
08
Which of the following option(s) is (are) true about the moment generating function of the random variable
Y
Y
Y
?
Comprehension
HARD
3 marks
24 December 2023
09
Let
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d. Binomial
(
5
,
1
2
)
X_1, X_2, X_3, X_4 \sim \text{i.i.d. Binomial}\left(5, \frac{1}{2}\right)
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d. Binomial
(
5
,
2
1
)
. Define another random variable
Z
=
Max
(
X
1
,
X
2
,
X
3
,
X
4
)
Z = \text{Max}(X_1, X_2, X_3, X_4)
Z
=
Max
(
X
1
,
X
2
,
X
3
,
X
4
)
. Find
4
P
(
Z
≤
2
)
4P(Z \le 2)
4
P
(
Z
≤
2
)
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
03 September 2023
Showing 9 questions.
Complete question index for this section:
Question 1 (multiple):
Question 2 (comprehension):
Question 3 (comprehension):
Question 4 (integer):
Question 5 (comprehension):
Question 6 (comprehension):
Question 7 (single):
Question 8 (comprehension):
Question 9 (integer):
