STT211 List of Questions

Q1 A ____________________ random variable is memoryless

exponential

normal

gamma

uniform

Q2 If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

0.3681

0.5987

0.5732

0.4123

Q3 Let X have a standard gamma distribution with alpha =7. Compute P(X <4 or X>6)

0.671

0.535

0.713

0.824

Q4 Let X have a uniform distribution on the interval [A,B]. compute V(X)

$$ \frac {A-2B} {\sqrt {A}}$$

$$ \frac {2B-A} {\sqrt {12B}}$$

$$ \frac {4B-A} {\sqrt {3AB}}$$

$$ \frac {B-A} {\sqrt {12}}$$

Q5 Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation?

0.314

0.121

0.244

0.412

Q6 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective

0.578

0.322

0.661

0.472

Q7 A bus starts with 6 people and stops at 10 different stops, how many different ways can the 6 people depart if no two passenger can depart at the same bus stop ____

162000

178000

163200

151200

Q8 A set X has a elements, a second set Y has b elements and a third set Z has c element, the number element from the Cartesian product of the three set ________

abc

a+b+c

ab+3c

(2a+3c)/2b

Q9 A bus starts with 6 people and stops at 10 different stops, how many different ways can the 6 people depart if any passenger can depart at any bus stop ____

1000000

540

120

1200000

Q10 A special case of the gamma distribution in which λ =1/2and n replaced by n/2, where n is a positive integer is called the ________ distribution

standard

chi square

gamma

exponential

Q11 A coin is rolled thrice, what is the probability for an event that at least two head or at least two tails occurs?

(1/2)

(2/3)

(7/3)

(1/4)

Q12 Two petrol station are located in a street at Victoria island, each of the petrol station has 5 pumps, an experiment was carry out to determine the number of pumps in use at a particular time of the day at each of the petrol station, assume an experimental outcome is (x,y), where x specified the number of pumps in use at the 1st station and y the number of pumps in use at the second station. How many of such outcome will you have in this experiment?

24

10

12

36

Q13 The 3rd and 7th term of a G.P. are 81 and16 respectively, find the 1st and 5th term

250 and 43

729/4 and 36

120 and 24

402/5 and 53

Q14 How many runs of W do your have in the following sequences WWWLWWLLWLWWLLWWW

2

4

11

5

Q15 A student is to answer all the nine questions in an examination. It is believed that the sequence in which the questions are answered may have a considerable effect on the performance of the student. In how many different order can the question be answered

120200

360

362880

480

Q16 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective

0.578

0.322

0.661

0.472

Q17 A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(P|A)?

0.042

0.44

0.083

0.25

Q18 When you toss 5 coins once, if the number of head(s) is the random variable define on the resulting sample space. What is the set of random variable resulting from this experiment?

{1,2,3,4,5}

{2,4,5}

{2,3,4,5}

{0,1,2,3,4,5}

Q19 Evaluate (x-2)!(y-4) if x=6 and y=9

120

60

124

30

Q20 Set X has 8 elements and set Y has 10 elements, if there are 5 common elements in X and Y, what is the cardinality of X union Y?.

6

13

15

19

Q21 A ____________________ random variable is memoryless

exponential

normal

gamma

uniform

Q22 If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

0.3681

0.5987

0.5732

0.4123

Q23 Let X have a standard gamma distribution with alpha =7. Compute P(X <4 or X>6)

0.671

0.535

0.713

0.824

Q24 Let X have a uniform distribution on the interval [A,B]. compute V(X)

$$ \frac {A-2B} {\sqrt {A}}$$

$$ \frac {2B-A} {\sqrt {12B}}$$

$$ \frac {4B-A} {\sqrt {3AB}}$$

$$ \frac {B-A} {\sqrt {12}}$$

Q25 Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation?

0.314

0.121

0.244

0.412

Q26 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective

0.578

0.322

0.661

0.472

Q27 A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(P|A)?

0.042

0.44

0.083

0.25

Q28 When you toss 5 coins once, if the number of head(s) is the random variable define on the resulting sample space. What is the set of random variable resulting from this experiment?

{1,2,3,4,5}

{2,4,5}

{2,3,4,5}

{0,1,2,3,4,5}

Q29 Evaluate (x-2)!(y-4) if x=6 and y=9

120

60

124

30

Q30 Set X has 8 elements and set Y has 10 elements, if there are 5 common elements in X and Y, what is the cardinality of X union Y?.

6

13

15

19

Q31 A coin is rolled thrice, what is the probability for an event that at least two head or at least two tails occurs?

(1/2)

(2/3)

(7/3)

(1/4)

Q32 Two petrol station are located in a street at Victoria island, each of the petrol station has 5 pumps, an experiment was carry out to determine the number of pumps in use at a particular time of the day at each of the petrol station, assume an experimental outcome is (x,y), where x specified the number of pumps in use at the 1st station and y the number of pumps in use at the second station. How many of such outcome will you have in this experiment?

24

10

12

36

Q33 The 3rd and 7th term of a G.P. are 81 and16 respectively, find the 1st and 5th term

250 and 43

729/4 and 36

120 and 24

402/5 and 53

Q34 How many runs of W do your have in the following sequences WWWLWWLLWLWWLLWWW

2

4

11

5

Q35 A bus starts with 6 people and stops at 10 different stops, how many different ways can the 6 people depart if any passenger can depart at any bus stop ____

1000000

540

120

1200000

Q36 A special case of the gamma distribution in which λ =1/2and n replaced by n/2, where n is a positive integer is called the ________ distribution

standard

chi square

gamma

exponential

Q37 Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation?

0.314

0.121

0.244

0.412

Q38 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective

0.578

0.322

0.661

0.472

Q39 A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A)= 0.6 and P(B) =0.05. What is P(P|A)?

0.042

0.44

0.083

0.25

Q40 When you toss 5 coins once, if the number of head(s) is the random variable define on the resulting sample space. What is the set of random variable resulting from this experiment?

{1,2,3,4,5}

{2,4,5}

{2,3,4,5}

{0,1,2,3,4,5}

Q41 A ____________________ random variable is memoryless

exponential

normal

gamma

uniform

Q42 If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?

0.3681

0.5987

0.5732

0.4123

Q43 Let X have a standard gamma distribution with alpha =7. Compute P(X <4 or X>6)

0.671

0.535

0.713

0.824

Q44 Let X have a uniform distribution on the interval [A,B]. compute V(X)

$$ \frac {A-2B} {\sqrt {A}}$$

$$ \frac {2B-A} {\sqrt {12B}}$$

$$ \frac {4B-A} {\sqrt {3AB}}$$

$$ \frac {B-A} {\sqrt {12}}$$

Q45 Each of 12 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerator is running. Suppose that 7 of these refrigerator have defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order. Let X be the number among the first 6 examined that have a defective compressor. What is the probability that X exceeds its mean value by more than 1 standard deviation?

0.314

0.121

0.244

0.412

Q46 Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components. 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0.1, and 2 defective components being in the batch under the condition that neither tested component is defective

0.578

0.322

0.661

0.472

Q47 A bus starts with 6 people and stops at 10 different stops, how many different ways can the 6 people depart if no two passenger can depart at the same bus stop ____

162000

178000

163200

151200

Q48 A set X has a elements, a second set Y has b elements and a third set Z has c element, the number element from the Cartesian product of the three set ________

abc

a+b+c

ab+3c

(2a+3c)/2b

Q49 A bus starts with 6 people and stops at 10 different stops, how many different ways can the 6 people depart if any passenger can depart at any bus stop ____

1000000

540

120

1200000

Q50 A special case of the gamma distribution in which λ =1/2and n replaced by n/2, where n is a positive integer is called the ________ distribution

standard

chi square

gamma

exponential

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