Week 1 Statistics 2 Questions

Q1

Enter the correct option number for

A

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q2

Enter the correct option number for

B

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q3

Enter the correct option number for

C

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q4

Enter the correct option number for

D

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q5

Enter the correct option number for

E

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q6

Enter the correct option number for

F

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q7

Find the value of

f_Y(0)

. Enter the answer correct to two decimal places.

Integer answerOCTOBER 26, 2025

OCTOBER 26, 2025

Q8

If

P(X_1>3)=\frac{t}{64}

, then find the value of

t

.

ComprehensionOCTOBER 26, 2025

OCTOBER 26, 2025

Q9

The joint PMF of two discrete random variables

X

and

Y

is given by

f_{XY}(x,y)=\frac{2x+3y+1}{14},\quad x,y\in\{0,1\},

and

0

otherwise. What is the value of

P(0<X\le 1\mid Y>0)

? Enter the answer correct to one decimal place.

Integer answerJULY 13, 2025

JULY 13, 2025

Q10

What are the values of

a

,

b

, and

c

?

Single correctJULY 13, 2025

JULY 13, 2025

Q11

From a well-shuffled deck of

52

cards, four cards are randomly selected without replacement. Let the random variable

X

represent the number of queens drawn, and let

Y

represent the number of red cards drawn. Find

P(X=2\mid Y=2)

.

Single correctFEBRUARY 23, 2025

FEBRUARY 23, 2025

Q12

Identify the correct joint PMF table of

X

and

Y

.

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Q13

What is the marginal distribution of

X

?

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Q14

Find the probability that the factory will produce at most

3

defective light bulbs in a batch of

5

light bulbs. Enter the answer correct to two decimal places.

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Q15

Find the value of

P(X\le4\mid X>1)

.

ComprehensionFEBRUARY 23, 2025

FEBRUARY 23, 2025

Q16

What is the marginal distribution of

X

?

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Q17

What is the conditional distribution of

Y\mid X=x

?

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Q18

Find the values of

m

and

n

.

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Q19

Find the value of

P(X=2\mid Y=9)

. Enter the answer correct to one decimal place.

ComprehensionOCTOBER 27, 2024

OCTOBER 27, 2024

Q20

If

P(X_1>2)=\frac{t}{9}

, then find the value of

t

.

Integer answerOCTOBER 27, 2024

OCTOBER 27, 2024

Q21

The joint PMF of two discrete random variables

X

and

Y

is given by the following table. Select the correct options from the following.

Multiple correctJULY 07, 2024

JULY 07, 2024

Q22

What is the probability that a player will choose a character equipped with a sword? Enter the answer correct to two decimal places.

ComprehensionJULY 07, 2024

JULY 07, 2024

Q23

What is the probability that a player chooses a warrior character with the staff? Enter the answer correct to two decimal places.

ComprehensionJULY 07, 2024

JULY 07, 2024

Q24

Find the probability

P(X=1,Y=1)

. Enter the answer correct to two decimal places.

ComprehensionJULY 07, 2024

JULY 07, 2024

Q25

Naveen tosses a fair coin twice and Suman tosses another fair coin two times. Let the random variables

X

and

Y

denote the number of heads observed by Naveen and Suman respectively. Identify the correct joint PMF table of

X

and

Y

.

Single correctFEBRUARY 25, 2024

FEBRUARY 25, 2024

Q26

What is the range of

X

?

ComprehensionFEBRUARY 25, 2024

FEBRUARY 25, 2024

Q27

What is the probability that the first failed inspection occurs on the analyst's

5^{\text{th}}

inspection? Enter the answer correct to three decimal places.

ComprehensionFEBRUARY 25, 2024

FEBRUARY 25, 2024

Q28

Find the value of

P(X=0\mid Z=1)

. Enter the answer correct to one decimal place.

ComprehensionFEBRUARY 25, 2024

FEBRUARY 25, 2024

Q29

Suppose

X\sim\operatorname{Bernoulli}(\frac{1}{3})

,

Y\sim\operatorname{Bernoulli}(\frac{1}{2})

, and

Z\sim\operatorname{Bernoulli}(\frac{2}{3})

such that

f_{XYZ}(0,0,1)=\frac{1}{4}

and

f_{Z|Y=1}(0)=\frac{1}{3}

. Find the value of

f_{X|Y=0,Z=1}(0)

. Enter the answer correct to two decimal places.

Integer answerOCTOBER 29, 2023

OCTOBER 29, 2023

Q30

Identify the correct joint PMF table of

X

and

Y

.

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

Q31

Find

P(X+Y\le2\mid X>0)

. Enter the answer correct to two decimal places.

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

Q32

If

P(U=a\mid U\ge1)=\frac{2}{5}

, then find the value of

a

.

ComprehensionOCTOBER 29, 2023

OCTOBER 29, 2023

Q33

The joint PMF of two discrete random variables

X

and

Y

is given in the following table. Which of the following options is correct?

Single correctJULY 16, 2023

JULY 16, 2023

Q34

Let

X\sim\operatorname{Binomial}(n,p)

. If the expected value and variance of

X

are

2

and

\frac{3}{2}

respectively, find the value of

P(X=2)

.

Single correctJULY 16, 2023

JULY 16, 2023

Q35

Identify the correct joint PMF table of

X

and

Y

.

ComprehensionJULY 16, 2023

JULY 16, 2023

Q36

Find

P(\frac{1}{2}<X<\frac{5}{2}\mid X>1)

. Enter the answer correct to two decimal places.

ComprehensionJULY 16, 2023

JULY 16, 2023

Q37

Find the value of

P(X=1\mid Z=5)

. Enter the answer correct to two decimal places.

ComprehensionJULY 16, 2023

JULY 16, 2023

Q38

Find the value of

n

for which

\frac{1}{30}P(X=3)=P(X=2)

.

ComprehensionJULY 16, 2023

JULY 16, 2023

Q39

Find the values of

c

and

d

.

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

Q40

Which among the following can be the joint PMF of

X

and

Y

?

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

Q41

Find

P(Y\ge 1\mid X=1)

.

ComprehensionOCTOBER 16, 2022

OCTOBER 16, 2022

Q42

A coin is biased so that the probability of obtaining a head is

0.75

. The coin is tossed four times and the number of heads obtained is given by

X

. Find

\operatorname{Var}(X)

. Enter the answer correct to two decimal places.

Integer answerJUNE 05, 2022

JUNE 05, 2022

Q43

Let

X

be a discrete random variable with PMF

p_X(1)=a

,

p_X(2)=b

,

p_X(3)=c

,

p_X(4)=0.3

, and

0

otherwise. Its CDF is

F_X(x)=0

for

x<1

,

0.2

for

1\le x<2

,

0.6

for

2\le x<3

,

0.7

for

3\le x<4

, and

d

for

x\ge4

. Evaluate

a+b+c+d

.

Integer answerJUNE 05, 2022

JUNE 05, 2022

Q44

Find the value of

\frac{1}{P(X\le 1, Y=0)+P(X=2,Y=1)}

.

Integer answerJUNE 05, 2022

JUNE 05, 2022

All questions