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IITM BS Week 10 Statistics 1 Questions | Prasnya
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22Q
01
Rohit wants to open his door with 5 keys (out of which 1 will open the door) and tries the keys independently and at random. If unsuccessful keys are eliminated from further selection, then find the expected number of trials required to open the door.
Numerical
MEDIUM
4 marks
10 May 2026
02
Let X and Y be two random variables. Choose all the correct statements from the following:
Multiple correct
MEDIUM
2 marks
10 May 2026
03
The probability mass function of a discrete random variable X is given by: Find the value of b such that
E
[
X
]
\mathbb{E}[X]
E
[
X
]
= 2.7. Enter the answer correct to one decimal place.
Numerical
HARD
4 marks
21 December 2025
04
The mean and variance of the observations x1, x2, x3, x4, x5 are 4 and 5 respectively. Suppose the mean and variance of the observations ax1+b, ax2+b, ax3+b, ax4+b, ax5+b are 16 and 45 respectively. Find the value of a+b, where a > 0.
Numerical
MEDIUM
3 marks
31 August 2025
05
Let X be a random variable with
E
[
X
]
\mathbb{E}[X]
E
[
X
]
= 5 and
Var
(
X
)
\operatorname{\operatorname{Var}}(X)
Var
(
X
)
= 9. Define a new random variable Y = aX - b where a and b are constants with a > 0. Find the value of b such that
E
[
Y
]
\mathbb{E}[Y]
E
[
Y
]
= 0 and
Var
(
Y
)
\operatorname{\operatorname{Var}}(Y)
Var
(
Y
)
= 1. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
31 August 2025
06
Find the value of
E
[
6
X
−
2
]
\mathbb{E}[6X - 2]
E
[
6
X
−
2
]
.
Comprehension
MEDIUM
2 marks
13 April 2025
07
Find the value of
Var
(
3
X
−
4
)
\operatorname{\operatorname{Var}}(3X - 4)
Var
(
3
X
−
4
)
.
Comprehension
MEDIUM
2 marks
13 April 2025
08
Find the value of
E
[
Y
2
+
5
Y
]
\mathbb{E}[Y^2 + 5Y]
E
[
Y
2
+
5
Y
]
.
Comprehension
MEDIUM
4 marks
22 December 2024
09
Find the value of
Var
(
Y
)
\operatorname{\operatorname{Var}}(Y)
Var
(
Y
)
. [Enter the correct answer up to 2 decimal places]
Comprehension
EASY
2 marks
22 December 2024
10
The probability mass function of a discrete random variable X is given by Table 2. Find the value of
E
[
X
2
−
1
]
\mathbb{E}[X^2 - 1]
E
[
X
2
−
1
]
.
Single correct
MEDIUM
3 marks
01 September 2024
11
What is the value of
E
[
X
2
]
\mathbb{E}[X^2]
E
[
X
2
]
?
Comprehension
MEDIUM
3 marks
01 September 2024
12
Find the standard deviation of X.
Comprehension
EASY
2 marks
01 September 2024
13
Find the value of
Var
(
X
)
\operatorname{\operatorname{Var}}(X)
Var
(
X
)
in terms of p.
Comprehension
MEDIUM
3 marks
01 September 2024
14
What is the value of
E
[
3
X
+
2
]
\mathbb{E}[3X + 2]
E
[
3
X
+
2
]
?
Comprehension
EASY
2 marks
01 September 2024
15
The probability mass function of a discrete random variable X is given by: Find the value of
E
[
2
X
+
1
]
\mathbb{E}[2X + 1]
E
[
2
X
+
1
]
^2. Enter the answer correct to two decimal places. *Note for reference, the PMF table is:* x │ -1 │ 0 │ 1 P(X=x) │
1
6
\frac{1}{6}
6
1
│
1
2
\frac{1}{2}
2
1
│
1
3
\frac{1}{3}
3
1
Numerical
MEDIUM
3 marks
28 April 2024
16
Find the expected value of X. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
28 April 2024
17
Six men and five women apply for a position of administrative in a company and two of the applicants are selected for the interview. If the random variables X and Y denote the number of male and number of female in the interview pool respectively, then calculate the value of
E
[
X
+
Y
]
\mathbb{E}[X + Y]
E
[
X
+
Y
]
.
Single correct
EASY
4 marks
24 December 2023
18
Find
E
[
X
]
\mathbb{E}[X]
E
[
X
]
. (Enter the answer correct to 2 decimal places). Using the PMF of X:
E
[
X
)
=
2
⋅
(
1
/
9
)
+
3
⋅
(
1
/
9
)
+
4
⋅
(
13
/
36
)
+
5
⋅
(
1
/
6
)
+
6
⋅
(
1
/
4
)
E
(
X
)
=
2
/
9
+
3
/
9
+
52
/
36
+
5
/
6
+
6
/
4
E
(
X
)
=
5
/
9
+
13
/
9
+
5
/
6
+
3
/
2
E
(
X
]
=
18
9
+
5
6
+
9
6
\mathbb{E}[X) = 2 \cdot (1/9) + 3 \cdot (1/9) + 4 \cdot (13/36) + 5 \cdot (1/6) + 6 \cdot (1/4) \mathbb{E}(X) = 2/9 + 3/9 + 52/36 + 5/6 + 6/4 \mathbb{E}(X) = 5/9 + 13/9 + 5/6 + 3/2 \mathbb{E}(X] = \frac{18}{9} + \frac{5}{6} + \frac{9}{6}
E
[
X
)
=
2
⋅
(
1/9
)
+
3
⋅
(
1/9
)
+
4
⋅
(
13/36
)
+
5
⋅
(
1/6
)
+
6
⋅
(
1/4
)
E
(
X
)
=
2/9
+
3/9
+
52/36
+
5/6
+
6/4
E
(
X
)
=
5/9
+
13/9
+
5/6
+
3/2
E
(
X
]
=
9
18
+
6
5
+
6
9
= 2 +
14
6
\frac{14}{6}
6
14
= 2 +
7
3
\frac{7}{3}
3
7
= 2 + 2.3333... ≈ 4.33.
Comprehension
MEDIUM
2 marks
03 September 2023
19
A random variable X has the following probability mass function: If
E
[
X
]
\mathbb{E}[X]
E
[
X
]
= 2, then what will be the value of x3?
Numerical
MEDIUM
3 marks
11 December 2022
20
Suppose a random variable Y represents the number of hours a student study in class on a particular day and the probability mass function of Y is given as: P(Y = y) = { 0.4 for
y
=
0
y = 0
y
=
0
; 0.2 for
y
=
1
y = 1
y
=
1
; 0.4 for
y
=
2
y = 2
y
=
2
; 0 otherwise } Find the value of
Var
(
Y
)
\operatorname{\operatorname{Var}}(Y)
Var
(
Y
)
(Enter the answer correct to 2 decimal accuracy).
Numerical
EASY
3 marks
11 December 2022
21
A fair coin is tossed three times. If X denote the number of heads followed immediately by a tail, then what is the expected value of X?
Single correct
MEDIUM
2 marks
07 August 2022
22
Six men and five women apply for a position of administrative in a company and two of the applicants are selected for the interview. If the random variables X and Y denote the number of male and number of female in the interview pool respectively, then calculate the value of
E
[
X
+
Y
]
\mathbb{E}[X + Y]
E
[
X
+
Y
]
.
Numerical
EASY
4 marks
07 August 2022
Showing 22 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (multiple):
Question 3 (integer):
Question 4 (integer):
Question 5 (integer):
Question 6 (comprehension):
Question 7 (comprehension):
Question 8 (comprehension):
Question 9 (comprehension):
Question 10 (single):
Question 11 (comprehension):
Question 12 (comprehension):
Question 13 (comprehension):
Question 14 (comprehension):
Question 15 (integer):
Question 16 (comprehension):
Question 17 (single):
Question 18 (comprehension):
Question 19 (integer):
Question 20 (integer):
Question 21 (single):
Question 22 (integer):
