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IITM BS Week 9 Statistics 2 Questions | Prasnya
Statistics 2 > Week 9
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27Q
01
Let
X
X
X
be a discrete random variable taking values
{
1
,
2
,
3
}
\{1, 2, 3\}
{
1
,
2
,
3
}
with respective probabilities
{
p
,
1
−
p
2
,
1
−
p
2
}
\left\{p, \frac{1-p}{2}, \frac{1-p}{2}\right\}
{
p
,
2
1
−
p
,
2
1
−
p
}
, where
0
≤
p
≤
1
0 \le p \le 1
0
≤
p
≤
1
is a parameter. Consider the samples
{
1
,
2
,
2
,
1
,
3
,
2
,
1
,
3
,
2
,
3
}
\{1, 2, 2, 1, 3, 2, 1, 3, 2, 3\}
{
1
,
2
,
2
,
1
,
3
,
2
,
1
,
3
,
2
,
3
}
from
X
X
X
. Using a
U
n
i
f
o
r
m
(
0
,
1
)
Uniform(0, 1)
U
ni
f
or
m
(
0
,
1
)
prior, find the posterior mean of
p
p
p
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
10 May 2026
02
Let
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d. Bernoulli
(
p
)
X_1, X_2, X_3, X_4 \sim \text{i.i.d. Bernoulli}(p)
X
1
,
X
2
,
X
3
,
X
4
∼
i.i.d. Bernoulli
(
p
)
. The prior distribution of
p
p
p
has the following PMF:. Find the posterior probability
P
(
P
=
0.8
∣
S
)
P(P = 0.8 \mid S)
P
(
P
=
0.8
∣
S
)
using Bayes' theorem. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
10 May 2026
03
Which of the following is the correct likelihood function
L
(
λ
)
L(\lambda)
L
(
λ
)
based on the given sample?
Comprehension
EASY
2 marks
10 May 2026
04
Find the posterior mean of
λ
\lambda
λ
using the given prior distribution. Enter the answer correct to one decimal place.
Comprehension
MEDIUM
3 marks
10 May 2026
05
Which of the following is the correct likelihood function
L
(
θ
)
L(\theta)
L
(
θ
)
based on the given sample?
Comprehension
EASY
2 marks
10 May 2026
06
Find the posterior mean of
θ
\theta
θ
using the given prior distribution. Enter the answer correct to one decimal place.
Comprehension
EASY
3 marks
10 May 2026
07
The company assumes a Beta(1.4, b) prior for p. Given that prior knowledge suggests the expected value of p is approximately 0.2, determine the appropriate value of b.
Comprehension
EASY
2 marks
13 April 2025
08
Using the prior distribution and the observed data, compute the posterior distribution of p.
Comprehension
EASY
1 marks
13 April 2025
09
Assume the prior distribution of
λ
\lambda
λ
to be Gamma(3, 2). Determine the posterior distribution of
λ
\lambda
λ
.
Comprehension
MEDIUM
2 marks
13 April 2025
10
Find the posterior distribution of
p
p
p
for a
Beta
[
3
,
2
]
\text{Beta}[3, 2]
Beta
[
3
,
2
]
prior.
Comprehension
MEDIUM
3 marks
22 December 2024
11
Find the posterior mean using the correct prior from the previous question. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
22 December 2024
12
Find the posterior distribution of
Θ
\Theta
Θ
.
Comprehension
MEDIUM
3 marks
01 September 2024
13
Find the posterior mean. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
01 September 2024
14
Find the posterior distribution of
θ
\theta
θ
.
Comprehension
MEDIUM
3 marks
28 April 2024
15
Find the posterior mean. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
28 April 2024
16
Find the posterior distribution of
p
p
p
for a
Uniform
[
0
,
1
]
\text{Uniform}[0, 1]
Uniform
[
0
,
1
]
prior.
Comprehension
EASY
3 marks
24 December 2023
17
Find the posterior mean. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
24 December 2023
18
Let
X
X
X
be a discrete random variable taking values
{
0
,
1
,
2
}
\{0, 1, 2\}
{
0
,
1
,
2
}
with respective probabilities
{
p
3
,
(
1
−
p
)
,
2
p
3
}
\{\frac{p}{3}, (1-p), \frac{2p}{3}\}
{
3
p
,
(
1
−
p
)
,
3
2
p
}
, where
0
≤
p
≤
1
0 \le p \le 1
0
≤
p
≤
1
is a parameter. Consider the samples
{
2
,
1
,
1
,
0
,
0
,
2
,
1
,
2
,
0
,
2
}
\{2, 1, 1, 0, 0, 2, 1, 2, 0, 2\}
{
2
,
1
,
1
,
0
,
0
,
2
,
1
,
2
,
0
,
2
}
from
X
X
X
. Using a
Uniform
[
0
,
1
]
\text{Uniform}[0,1]
Uniform
[
0
,
1
]
prior, find the posterior mean of
p
p
p
. Enter the answer correct to two decimal places.
Numerical
MEDIUM
3 marks
03 September 2023
19
Find the posterior distribution of
θ
\theta
θ
.
Comprehension
MEDIUM
3 marks
03 September 2023
20
Find the posterior mean. Enter the answer correct to two decimal places.
Comprehension
EASY
2 marks
03 September 2023
21
Find the posterior distribution of p.
Comprehension
MEDIUM
3 marks
30 April 2023
22
Find the posterior mean. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
30 April 2023
23
Out of 10 throws, if four appeared a total of five times, find the posterior distribution of p.
Comprehension
EASY
3 marks
11 December 2022
24
Find the posterior mean using the given prior. Enter the answer correct to one decimal place.
Comprehension
EASY
2 marks
11 December 2022
25
Find the value of
α
\alpha
α
and
β
\beta
β
.
Comprehension
MEDIUM
2 marks
07 August 2022
26
Find the posterior mean of
λ
\lambda
λ
for the given sample. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
07 August 2022
27
Using a Uniform[0,1] prior, find the posterior mean of the given sample. Enter the answer correct to three decimal places.
Comprehension
HARD
2 marks
07 August 2022
Showing 27 questions.
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Question 18 (integer):
Question 19 (comprehension):
Question 20 (comprehension):
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Question 24 (comprehension):
Question 25 (comprehension):
Question 26 (comprehension):
Question 27 (comprehension):
