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STA2204

ASSIGNMENT 1

DUE DATE: 2 FEB 2016 (1FN1/1HR1, 1BA1/1IB2), 4 FEB 2016 (1AC1/1MK1)

Answer ALL 4 questions.

1. Records of a private university show that 30% of the students stay off campus.

(a) In a random sample of 6 students, what is the probability that more than 3 of them stay off campus? (3 marks)

(b) What is the probability that out of a random sample of 8 students, less than 2 of them DO NOT stay off campus? (3 marks)

2. The number of car accidents per day on a particular stretch of road follows a Poisson distribution with mean 1.5.

(a) What is the probability that there will be at most two accidents occur in one day? (3 marks)

(b) What is the probability that there will be more than one accident occur in one week? (4 marks)

3. The probability distribution of discrete random variable X is as follow:

[pic] , [pic]

[pic] [pic] , [pic]

0 , otherwise

(a) Find the value of k. (2 marks)

(b) Calculate [pic]. (2 marks)

(c) Calculate [pic] (4 marks)

4. John receives a set of four keys from his form teacher to open a door. He tries to open the door by choosing a key one by one at random without repetition. Let X represents the number of keys John has to try to open the door.

(a) Using a tree diagram or otherwise, list down all the possible outcomes of the above situation. Write down the possible value of X for each outcome. Hence, construct the probability distribution of X. (4 marks)

i) Calculate the value of E(2X – 1). (3 marks)