S2 Revision Quiz Answers coming up…. Question 1 (3 points) A string AB of length 5 cm is cut, in a random place C, into two pieces. The random variable.

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Acknowledgement: Thanks to Professor Pagano

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Presentation transcript:

S2 Revision Quiz Answers coming up…

Question 1 (3 points) A string AB of length 5 cm is cut, in a random place C, into two pieces. The random variable X is the length of AC. Write down the name of the probability distribution of X and sketch the graph of its probability density function

Question 2 (3 marks) X ~ R[0, 5] Find E(X) and Var(X)

Question 3 (1 mark) X ~ R[0, 5] Find P(X > 3)

Question 4 (1 mark) X ~ R[0, 5] Find P(X = 3)

Question 5 (1 mark) An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour. Suggest a suitable model for the number of faulty parts per hour

Question 6 (2 marks) An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour. Describe two assumptions that are necessary to model the number of faulty parts using a Poisson Distribution.

Question 7 (2 marks) An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour. Find the probability of 2 faulty parts being detected in a 1 hour period.

Question 8 (3 marks) An engineering company makes an electrical parts. At the end of the process each part is checked to see if it is faulty. Faulty parts are detected at a rate of 1.5 per hour. Find the probability of at least one faulty part being detected in a 3 hour period.

Question 9 (3 marks) A bag contains a large number of coins: 75% are 10p coins 25% are 5p coins Write down all the possible combinations of 3 coins that you could select from the bag

Question 10 (1 mark) A bag contains a large number of coins: 75% are 10p coins 25% are 5p coins Write down the possible medians of all the samples of 3 coins that you could select from the bag

Question 11 (3 marks) A bag contains a large number of coins: 75% are 10p coins 25% are 5p coins A random sample of 3 coins is selected. Find the sampling distribution for the median of the values of the 3 selected coins.

Question 12 (2 marks) Write down the 2 conditions under which the Poisson distribution may be used as an approximation to the Binomial distribution.

Question 13 (2 marks) A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01 Find the probability that 2 consecutive calls will be wrongly connected.

Question 14 (3 marks) A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01 Find the probability that more than 1 in 5 consecutive calls will be wrongly connected.

Question 15 (3 marks) A call centre routes telephone calls. The probability of a call being wrongly connected is 0.01 The call centre receives 1000 calls each day. Find the mean and variance of the number of incorrectly connected calls.

Question 16 (2 marks) A call centre routes telephone calls. The probability of a call being wrongly connected is The call centre receives 1000 calls each day. Use a Poisson approximation to find the probability that more than 6 calls each day are wrongly connected. Give your answer to 3 dp.

Question 17 (2 marks) Write down 2 conditions for a Normal distribution to be used to approximate a Binomial distribution.

Question 18 (2 marks) A Normal distribution is to be used to approximate a Binomial distribution. Write down the mean and variance of this normal approximation in terms of n and p.

Question 19 (5 marks) A factory makes 2000 DVDs each day. 3% of all DVDS made are faulty. Use a normal approximation to estimate the probability that at least 40 faulty DVDs are produced in a day.

Question 20 (3 marks) A factory makes 2000 DVDs each day. 3% are faulty It costs £0.70 to make each DVD. Non-faulty DVDs are sold for £11 each. Faulty DVDs are destroyed Find the expected profit made by the factory per day.

Question 21 (3 marks) Sketch the probability density function of X

Question 22 (1 mark) What is the mode of X?

Question 23 (7 marks) Specify fully the cumulative distribution function of X

Question 24 (3 marks) Find the median of X using your answer for F(x)