Statistics for Data Science II · Quiz 1 · Jan 2026

The number of people

who make a reservation in a restaurant on a particular day is a random variable with mean equal to 10 and variance equal to 5. Find a lower bound on the probability that on a particular day, number of reservations made will lie in between 5 and 15 using Chebyshev's inequality. Enter the answer correct to two decimal places.

Let

and

be three random variables with Cov

, Cov

, Cov

, Var

Define the new random variables

and

. Find the value of Cov

.

At a bank, the time

(in minutes) that a customer waits to be served is a continuous random variable with probability density function

Find the value of

.

A delivery company operates two independent service counters A and B. Let

and

denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of

and

is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for

.

A delivery company operates two independent service counters A and B. Let

and

denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of

and

is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for

.

A delivery company operates two independent service counters A and B. Let

and

denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of

and

is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for

.

A delivery company operates two independent service counters A and B. Let

and

denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of

and

is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Enter the correct option number for

.

A delivery company operates two independent service counters A and B. Let

and

denote the number of parcels processed by counters A and B in one hour, respectively. The joint probability mass function of

and

is given as:

To assess workload, the management defines the hourly load index as the maximum number of parcels processed by counters A and B in a given hour. Find the probability that the hourly load index is equal to the number of parcels processed by counter A.

Calculate the value for

. Enter the answer correct to one decimal place.

A box contains one red ball and one blue ball. Two balls are drawn one after another with replacement and the colour of each ball drawn is recorded. Let • A be the number of times a red ball is drawn in the two draws. • B be the number of times a blue ball is drawn in the two draws. Choose the correct statement(s) from the following.

The number of vehicles (

) passing a signal in a day follows a Poisson distribution with parameter

. Each vehicle independently violates traffic rules with probability 0.1. Let

denote the number of vehicles violating traffic rules in a day. Based on the above data, answer the given subquestions.

Which of the following option(s) is/are true?

The number of vehicles (

) passing a signal in a day follows a Poisson distribution with parameter

. Each vehicle independently violates traffic rules with probability 0.1. Let

denote the number of vehicles violating traffic rules in a day. Based on the above data, answer the given subquestions.

Find the value of Var(2X)−3Var(Y ) + 4.

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable

denote the number of books sold in an hour. The probability mass function of

is given by:

The store defines a discount indicator

as:

Based on the above data, answer the given subquestions.

Find the value of

. Enter the answer correct to two decimal places.

A small bookstore tracks the number of books sold in an hour. Let a discrete random variable

denote the number of books sold in an hour. The probability mass function of

is given by:

The store defines a discount indicator

as:

Based on the above data, answer the given subquestions.

Find the value of

. Enter the answer correct to two decimal places.

A fair coin is tossed three times. Let

denote the number of heads in the first toss and

be the total number of heads obtained across all three tosses. Based on this, answer the given sub questions:

Find the value of

.

A fair coin is tossed three times. Let

denote the number of heads in the first toss and

be the total number of heads obtained across all three tosses. Based on this, answer the given sub questions:

Find the value of

. Enter the answer correct to three decimal places.

The joint PMF of two discrete random variables

and

is given as:

Based on the above data, answer the given subquestions.

Find the value of

.

The joint PMF of two discrete random variables

and

is given as:

Based on the above data, answer the given subquestions.

Find the value of

.

The amount of rainfall

(in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function

Based on the above data, answer the given subquestions.

Which of the following options correctly represents the probability density function of

?

The amount of rainfall

(in cm) on a randomly chosen rainy day in a city is a continuous random variable with cumulative distribution function

Based on the above data, answer the given subquestions.

Find the value of

.