Week 2 Statistics 2 Questions

01

The joint probability mass function of two discrete random variables

X

and

Y

is given by

f_{XY}(x,y)=\begin{cases}\dfrac{xy}{36}, & x,y\in\{1,2,3\},\\ 0, & \text{otherwise.}\end{cases}

What is the value of

P(X+Y=4)

? Enter the answer correct to two decimal places.

Numerical

MEDIUM

3 marks

06 April 2026

02

Let

X

be a discrete random variable with PMF as follows. Suppose

X_1, X_2 \sim

i.i.d.

X

. Define

Y=X_1+X_2

. Which of the following option(s) is/are true about the moment generating function of

Y

?

Multiple correct

MEDIUM

3 marks

03 August 2025

03

Let

X\sim\mathrm{Uniform}\{1,2\}

be discrete. Let

(Y\mid X=1)\sim\mathrm{Exp}(1)

and

(Y\mid X=2)\sim\mathrm{Exp}(2)

. Find the distribution of

Y

.

Single correct

MEDIUM

3 marks

16 March 2025

04

The joint PMF table of two discrete random variables

X_1

and

X_2

is given. Which option(s) is/are true?

Multiple correct

MEDIUM

3 marks

16 March 2025

05

Calculate

F_Z(3)

. Enter the answer correct to two decimal places.

Comprehension

EASY

4 marks

16 March 2025

06

Find the range of

Z

.

Comprehension

EASY

1 marks

01 December 2024

07

Find

P(Z=3)

.

Comprehension

EASY

2 marks

01 December 2024

08

Which of the following option(s) is/are true? The joint PMF table of two discrete random variables

X_1

and

X_2

is given as:

Multiple correct

MEDIUM

3 marks

24 March 2024

09

Let

X, Y, Z \sim \text{i.i.d. Geometric}(1/2)

. Define a new random variable

U = \min(X, Y, Z)

. What is the value of

1/P(U \ge 3)

?

Numerical

MEDIUM

3 marks

06 August 2023

10

Suppose

X \sim \text{Bernoulli}(0.4)

and

Y\mid X=x \sim \text{Uniform}(x-1,x+1)

. Find the density of

Y

.

Single correct

MEDIUM

3 marks

06 August 2023

11

Let

(X,Y)\sim \text{Uniform}(D)

. Which of the following may represent a region

D

such that

X

and

Y

are independent?

Single correct

MEDIUM

3 marks

06 August 2023

12

Find the range of

Z

.

Comprehension

EASY

1 marks

02 April 2023

13

Find the value of

P(0<Z<3)

.

Comprehension

MEDIUM

2 marks

02 April 2023

14

Find the range of

Z

.

Comprehension

EASY

1 marks

20 November 2022

15

Find the probability mass function (PMF) of

Z

.

Comprehension

MEDIUM

3 marks

20 November 2022

All PYQs

All PYQs

All PYQs

All PYQs