wsw9-Graded_Assignment_Sep_2025_Statistics_I_Qualifier

Graded Assignment - (Sep 2025 - Statistics I - Qualifier)

The due date for submitting this assignment has passed. Due on 2025-11-26, 23:59 IST. You may submit any number of times before the due date. The final submission will be considered for grading.

Last Submitted: You have last submitted on: 2025-11-26, 20:35 IST

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Question 1

A discrete random variable $X$ can take the values 1,2,···,14. For these values the cumulative distribution function is defined by:$F(x)=P(X\le x)=\frac{x^2+k}{253}$; $x$= 1,2,···,14. Find the value of $k$. Your Answer: 57

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 57

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Question 2

An organization in Texas organizes lucky draw this month. 5 thousand tickets are sold for 2$each.Eachhasanequalchanceofwinning.1ticketswillwin1077$, 3 tickets will win 507$and11ticketswillwin109$. Let, the random variable $X$ denote the net gain from purchase of one ticket. What is the probability that $X$ takes the value less than 507? (Enter the answer correct to 4 decimal place) Your Answer: 0.9998

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.9993,1.0000

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Question 3

In a group of 222 people, 15 are photographers and 207 are journalists. 9 people are randomly picked from a group of these 222 people. Let, $Y$ be a random variable which represents the number of photographers. How many possible values can the random variable $Y$ take? Your Answer: 10

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 10

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Question 4

Which of the following is/are discrete random variables?

• Number of tires produced in an automotive tire factory every 30 minutes.
• The number of kernels(pieces) of popcorn in a  $1kg$ container.
• The time between customers entering a checkout lane at a retail store.
• The amount of rain recorded at an airport one day.
• The amount of liquid in a $2litres$ bottle of soft drink.
• The number of no-shows for every $1000$ reservations made with a commercial airline.

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• Number of tires produced in an automotive tire factory every 30 minutes.
• The number of kernels(pieces) of popcorn in a  $1kg$ container.
• The number of no-shows for every $1000$ reservations made with a commercial airline.

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Question 5

A biased coin with probability of heads $0.75$ is tossed three times. Let $X$ be a random variable that represents the number of head runs, a head run being defined as a consecutive occurrence of at least two heads. Then the probability mass function of $X$ is given by:

• P(X=x)= \begin{cases} 0.375 & \text{for x= 0}\\ 0.625 & \text{forx = 1}\\ \end{cases}
• P(X=x)= \begin{cases} 0.297 & \text{for x= 0}\\ 0.703 & \text{forx = 1}\\ \end{cases}
• P(X=x)= \begin{cases} 0.016 & \text{for x= 0}\\ 0.140 & \text{forx= 1}\\ 0.422 & \text{forx= 2}\\ 0.422 & \text{forx = 3} \end{cases}
• P(X=x)= \begin{cases} 0.016 & \text{for x= 0}\\ 0.844 & \text{forx= 1}\\ 0.140 & \text{forx = 2}\\ \end{cases}

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• P(X=x)= \begin{cases} 0.297 & \text{for x= 0}\\ 0.703 & \text{forx = 1}\\ \end{cases}

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Question 6

Nina has 6 music sessions in a week. She attends the sessions 6 days a week 44% of the time, 5 days 17% of the time, one day 13% of the time, and no days 26% of the time. Let, $X$ be a discrete random variable representing the number of sessions she attends in a week. Suppose one week is randomly selected, what is the probability that the random variable $X$ take the value at most 5?(Enter the answer correct to 2 decimal places) Your Answer: 0.56

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.53,0.59

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Question 7

Find the value of k for which k${\left(\frac{4}{9}\right)}^x$( x = 0, 1, 2, …) is a pmf.(Enter the answer correct up to 2 decimal places) Your Answer: 0.56

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.53,0.59

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Question 8

Using the information in previous question, calculate $P(X=2)$.(Enter the answer correct up to 2 decimal places) Your Answer: 0.11

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Range) 0.08,0.14

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Question 9

From a box $A$ containing 3 white and 6 black balls, 5 balls are transferred into an empty box $B$. Let $X$ be a random variable that represents the number of white balls which are transferred from $A$ to $B$. What value of random variable will have the least probability? Your Answer: 0

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 0

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Question 10

The probability mass function of a random variable X is given by:

       $P(X=x)$= $\{\begin{array}{ll}3k^2-3k& \text{for }x=0\\ 2k^2-1& \text{for}x=1\\ 0& \text{otherwise}\end{array}$

 Determine the value of k given $k>0$. Your Answer: 1

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

(Type: Numeric) 1

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Question 11

A box contains 7 red balls and 5 blue balls. Four balls are drawn at random from the box without replacement. Let the random variable $X$ denote the number of red balls drawn. Find the possible values that $X$ can take.

• {1, 2, 3, 4}
• {1, 2, … , 7}
• {0, 1, 2, 3, 4}
• {0, 1, 2, … , 7}

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• {0, 1, 2, 3, 4}

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Question 12

What is the probability mass function of $X$?

• 
• 
• 
• 

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• 

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Question 13

What is the value of$P(X>2|X<5)$?

• $\frac{17}{36}$
• $\frac{21}{36}$
• $\frac{17}{21}$
• $\frac{23}{36}$

Status: Yes, the answer is correct. Score: 1

Accepted Answers:

• $\frac{17}{21}$

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