# Probability And Statistics | Week 3

Course Name: Probability And Statistics

#### These are Probability And Statistics Week 3 Assignment 3 Answers

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#### Q1. A random variable X has a discrete uniform distribution on the integers 0 through 9. Determine 9X the standard deviation of the random variable Y = 9X/2(A) 0.1562(B) 12.859(C) 12.9253(D) 0.6

Q2. Let X be a continuous random variable with the pdf f(x) = (1, 0 < x < 1 0, otherwise
Suppose Y = -2 log(X). Then find E(Y) and Median (Y).

(A) 2,2log 2
(B) 0.5, 2 loge 2
(C) 0.5, loge 2
(D) 2, loge 2

Answer: (A) 2,2log 2

These are Probability And Statistics Week 3 Assignment 3 Answers

Q3. In a manufacturing process, the probability, that a produced item is defective, is 0.05. What is the probability that out of nine successively produced items, only one is defective?
(A) (0.95)6 (0.05)
(B) 9 (0.95) * (0.05)6
(C) 9* (0.95)6* (0.05)
(D) (0.05)6 (0.95)

Answer: (C) 9* (0.95)6* (0.05)

Q4. The number of messages sent per hour over a computer network has the following distribution:

Determine the standard deviation of the number of messages sent per hour.
(A) 1.2
(B) 2.5
(C) 16.67
(D) 1.36

These are Probability And Statistics Week 3 Assignment 3 Answers

Q5. Since not all airline passengers show up for their reserved seat, an airline sells 122 tickets for a flight that can accommodate only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. What is the probability that every passenger who shows up can take the flight?
(A) 0.5
(B) 0.89792
(C) 0.789
(D) 0.9999

Q6. A large car showroom has 1000 cars on display. It is known that 50 cars have some defects. If quality inspector checks randomly 20 cars what is the mean and variance of the number of cars found defective during inspection.
(A) (0.1, 0.098)
(B) (1,0.932)
(C) (0.2, 0.49)
(D) (0.5, 1.24)

These are Probability And Statistics Week 3 Assignment 3 Answers

Q7. Suppose f(x) be a pdf of the form f(x) = ke-1/2|x-2|; -∞ < x < ∞, then what is the value of k?
(A) 1
(B) 1/4
(C) 1/2
(D) 2

Q8. In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.15. What is the probability that four or more people will have to be tested before two with the gene are detected?
(A) 0.0543
(B) 0.0856
(C) 0.04876
(D) 0.8148

These are Probability And Statistics Week 3 Assignment 3 Answers

Q9. A fair dice is rolled repeatedly. What is the probability that a 3 will show up before a 5 or 6?
(A) 2/3
(B) 1/6
(C) 1/2
(D) 1/3.

Q10. Assume that each of your calls to a popular radio station has a probability of 0.03 of connecting. that is, of not obtaining a busy signal. Assume that your calls are independent. What is the mean number of calls needed to connect?
(A) 100/3
(B) 3/100
(C) 18/100
(D) 19

These are Probability And Statistics Week 3 Assignment 3 Answers

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These are Probability And Statistics Week 3 Assignment 3 Answers

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