Section 5: Probability and Statistics

Q41. A fair die is rolled until a 1 appears. The probability that an odd number of rolls are needed is:

A. 1/6

B. 5/6

C. 6/11

D. 5/11

E. 1/2

Q42. If the distribution function F is given by then the density function of Y=15+2X is:

A.

B.

C.

D.

E.

Q43. The moment generating function for the normal distribution with mean and standard deviation is given by:

A.

B.

C.

D.

E.

Q44. Experience shows that the number of accidents on a particular road is distributed with a poisson distribution with a mean of 2 accidents per week. Using the central limit theorem what is the approximate probability that there will less than 100 accidents in a year.

A. 0.25

B. 0.33

C. 0.5

D. 0.67

E. 0.75

Q45. Assume the amount of rainfall recorded in a day is uniformly distributed on the interval (0,b). If a sample of 10 years’ records shows that the following amounts of rainfall were recorded on that date, compute using the method of moments and estimate of b. 0,0,0.7,1,0.1,0,0.2,0.5,0,0.6 measurements are in inches.

A. 0.42

B. 0.47

C. 0.52

D. 0.57

E. 0.62

Q46. If a die is thrown 50 times what is the expected number of sixes scored?

A. 8.33

B. 7.33

C. 6.33

D. 5.33

E. 4.33

Q47. The discrete random variable X takes the values 0 and 1 with probabilities of ½ each. The Probability Generating Function, Moment Generating Function and Standard deviation (in that order) are given by:

A.

B.

C.

D.

E.

Q48. The random variables X and Y are distributed with means and variances . The correlation coefficient of X and Y is . If Z=X+Y then the mean and variance of Z are:

A.

B.

C.

D.

E.

Q49. The mean, mean deviation, standard deviation and mid-spread of the observations 16, 5, 7, 13, 2, 9, 3, 20, 13, 6, 5 is:

A. 18, 5.73, 4.49, 8

B. 18, 4.73, 5.49, 8

C. 8, 4.73, 5.49, 18

D. 8, 5.49, 4.73, 18

E. 18, 4.73, 5.49, 18

Q50. Ignoring leap years what is the value of N such that the following probability is less than1/2: "The probability that none of a group of N or more randomly chosen people has a birthday on the same day as anyone else in the group"

A. 21

B. 22

C. 23

D. 24

E. 25