Statistics

Given following joint probability distribution table. Find E(X)-? 1/3 1/2 1 0 ¼

1/2

If P(A)=1/2 and P(B)=1/2 then 1/4, always 1/4, if A and B are independent 1/2, always 1/2, if A and B are independent None of the given answers

1/4, if A and B are independent

The fair dice is rolled. What is the probability of getting 5? 1/6 2/6 6 1 3/6

1/6

Given the following incomplete probability matrix, what is the joint probability of a good economy and no increase in interest rate? 5% 10% 20% 30%

10%

If a researcher wants to study a binomial population where p = 0.1, what is the minimum size n needed to make use of the central limit theorem? 0 100 10 10000 1000

100

Marks on a Chemistry test follow a normal distribution with an expectation of 65 and a mean square deviation of 12. Approximately what percentages of the students have scores below 50? 11% 89% 15% 18% 39%

11%

What is the mode of the returns for XYZ stock? 22% 11% 5% 2% 10%

11%

Assume the following probability density function for a random variable X: what is the variance of X? f(x) = x/18, 0≤x≤6 2 3.3 4.1 5.7

2

The table below shows the distribution of a random variable X. What is the var(X)? 2,01 1,67 4,71 0,7 4,7

2,01

Let X and Y be discrete random variables with joint probability function given by the following table:Find E(X)? 1 2.85 0.05 3.5 2.50

2.85

If var(X)=3, find var(-3X+4). 12 -5 19 27 -9

27

The Lakers scored the following numbers of goals in their last twenty matches: 3, 0, 1, 5, 4, 3, 2, 6, 4, 2, 3, 3, 0, 7, 1, 1, 2, 3, 4, 3. Which number had the highest frequency? 4 3 6 7 2

3

Rachel rolled a die forty five times with the following results: what was her mean score? 3.5 3.4 3.62 7.5 6.3

3.4

To apply the central limit theorem to the sampling distribution of the sample ean, the sample is usually considered to be large if n is greater than: 15 20 25 30

30

Possible outcomes for a discrete uniform distribution are the integers 2 to 9 inclusive. What is the probability of an outcome less than 5? 62.5% 37.5% 50.0% 100.0%

37.5%

A fair die was thrown 100 times. The frequency distribution is shown in the following table: how many throws scored greater than 2, but less than or equal to 5? 26 45 44 63 52

45

We are given the probability distribution functions of two random variables X and Y shown in the tables below. Find E[X+Y]. 5,8 2,2 2 8,8 10

5.8

Two extremely risky bonds have unconditional probabilities of default of 10% and 20%. Their correlation is 0.35. what is the probability that both bonds default? 2% 4.6% 6.2% 9.7%

6.2%

The table below shows the probability distribution function of a random variable X. If E[X]=5,3 find the value of x2. 3 1 8 7 10

7

What is the arithmetic mean for XYZ stock? 8.0% 7.3% 9.0% 11% 7%

7.3%

Find the probability of selecting a black card or a 6 from a deck of 52 playing cards 7/13 26/52 4/52 13/52 36/52

7/13

There are ten sprinters in the finals of a race. How many different ways can the gold, silver and bronze medals be awarded? 120 710 1440 100 60

710

Consider the following random variables:A standard normal random variable; no parameters needed;A Bernoulli variable that characterizes the probability of default (PD), where PD = 4%; A Poisson distribution that characterizes the number of defaults in a basket credit default swap, PD = 2%, n=50. which of the above has, respectively, the lowest value and highest value as its variance among the set? Standard normal (lowest) and Bernoulli (highest) Binomial (lowest) and Bernoulli (highest) Bernoulli (lowest) and Poisson (highest) Poisson (lowest) and Binomial (highest)

Bernoulli (lowest) and Poisson (highest)

Given following joint probability distribution table. Find cov(X,Y)-? 1/3 -1/4 1/2 0 1/4

-1/4

Which of the following represents the mean, standard deviation, and variance of a standard normal distribution? 1,2,4 1,1,1 0,1,1 1,2,0

0,1,1

Suppose that 10% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed? 0.031 0.053 0.098 0.0100 0.29

0.098

An auto insurance company insures drivers of all ages. An analyst compiled the following statistics on the company's insured drivers:A randomly selected driver that the company insures has an accident. Calculate the probability that the driver was age 16-20? 0.13 0.16 0.19 0.23 0.40

0.16

An insurance company examines its pool of auto insurance customers and gathers the following information:i) All customers insure at least one carii) 70% of the customers insure more than one cariii) 20% of the customers insure a sports carOf those customers who insure more than one car, 15% insure a sports car. What is the probability that a randomly selected customer insures exactly one car, and that car is not a sports car? 0.200 0.205 0.131 0.250 0.300

0.205

Heights of college women have a distribution that can be approximated by a normal curve with an expectation of 65 inches and a mean square deviation equal to 3 inches. About what proportion of college women are between 65 and 68 inches tall? 0.75 0.5 0.34 0.17 0.25

0.25

A random variable X has a probability distribution as follows: Then the probability that P(X < 2) is equal to 0.9 0.3 0.6 0.2 1

0.3

A recent study indicated that 60% of all businesses have a fax machine. Assuming binomial probability distribution, what is the probability that exactly four businesses will have a fax machine in a random selection of six businesses? 0.138 0.276 0.311 0.324

0.311

A bag contains blue and red balls. Two balls are drawn randomly without replacement. The probability of selecting a blue and then a red ball is 0.2. The probability of selecting a blue ball in the first draw is 0.5. What is the probability of drawing a red ball, given that the first ball drawn was blue? 0.4 0.2 0.1 0.5 0.3

0.4

A study of automobile accidents produced the following data: an automobile from one of the model years 1997, 1998, and 1999 was involved in an accident. Determine the probability that the model year of this automobile is 1997. 0.22 0.45 0.30 0.33 0.50

0.45

Two events each have probability 0.3 of occurring and are independent. The probability that neither occur is 0.49 0.51 0.3 0.6 none of the given answers

0.49

The number of days an employee is sick each month is modeled by a Poisson distribution with mean 1. The numbers of sick days in different months are mutually independent. Calculate the probability that an employee is sick more than two days in a three-month period. 0.199 0.224 0.577 0.423 0.801

0.577

You are given P[A v B] = 0.7 and . Determine P[A] 0.2 0.6 0.4 0.3 0.8

0.6

In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math? 0.67 0.40 0.60 0.33 0.50

0.67

Given a normal distribution with µ=90 and σ=10, what is the probability that X>75? 0.93 0.25 0.49 0.45 0.01

0.93

The sum of the probabilities of events A1, A2,..., An which form a sample space is equal to ... 1 0 ½ 1/5 1/3

1

A machine produces electrical components 99.7% of the components have lengths between 1.176 cm and 1.224 cm. Assuming this data is normally distributed, what are the mean and standard deviation? E(X)=1.210, std = 0.008 E(X) = 1.200, std = 0.008 E(X) = 1.120, std = 0.008 E(X) = 1.200, std = 0.004 E(X) = 1.1250, std = 0.004

E(X) = 1.200, std = 0.008

The table below shows the distribution of a random variable X. Find E[X] and var(X). E[X]= 0,2; VAR(X) =0.8 E[X]= 0,3; var(X) =0.27 E[X]= 0,2; var(X) =0.76 E[X]= 0,2; VAR(X) =0.21 E[X]= 0,8; VAR(X) =0.24

E[X]= 0,2; var(X) =0.76

Which of the following qualifies as a cumulative distribution function? F(1) = 0.5, F(2) = 0.25, F(3) = 0.25 F(1)=0, F(2) = 0.25, F(3) = 0.50, F(4)=1 F(1)=0, F(2) = 0.5, F(3) = 0.5, F(4) = 0. No right answer

F(1)=0, F(2) = 0.25, F(3) = 0.50, F(4)=1

Two uniquely possible events forming a complete group are ... Opposite Same Identically distributed Sample Density function

Opposite

The central limit theorem refers to which of the following characteristic of the sampling distribution of the sample mean? Regardless of the shape of the population's distribution, the sampling distribution of the sample mean from sufficiently large samples will be approximately normally distributed. Regardless of the shape of the population's distribution, the standard deviation of the sampling distribution of the sample mean from sufficiently large samples will be sigma/sqrt(n) Regardless of the shape of the population's distribution, the mean of the sampling distribution of the sample mean from sufficiently large samples will be equal to the mean of the population. As you take larger and larger sample from a normally distributed population, the standard deviation of the sampling distribution of the sample mean gets smaller and smaller.

Regardless of the shape of the population's distribution, the sampling distribution of the sample mean from sufficiently large samples will be approximately normally distributed.

Which of the following would not be categorized as a multivariate distribution? The return of a stock and the return of the DJIA The days a stock traded and the days it did not trade The returns of the stocks in the DJIA No right answer

The days a stock traded and the days it did not trade

Which of the following is the appropriate definition for the union of two events A and B? The set of all possible outcomes. The set of all basic outcomes contained within both A and B. The set of all basic outcomes in either A or B, or both. None of the given answers The set of all basic outcomes that are not in A and B.

The set of all basic outcomes in either A or B, or both.

Which of the following is the appropriate definition for the union of two events A and B? The set of all possible outcomes. The set of all basic outcomes contained within both A and B. The set of all basic outcomes in either A or B, or both. The set of all basic outcomes that are not in A and B.

The set of all basic outcomes in either A or B, or both.

Let X, and Y be the lifespans (in hours) of two electronic devices, and their joint probability density function is given below:. Determine the value of c c=6 c=3/2 c=12 c=1 c=2

c = 6

Which of these has a Geometric model? the number of aces in a five-card Poker hand the number of people we survey the number of people in a class of 25 who have taken Statistics the number of people we survey until we find someone who has taken Statistics

the number of people we survey until we find someone who has taken Statistics

Which of these has a Geometric model? the number of aces in a five-card Poker hand the number of people we survey the number of people in a class of 25 who have taken Statistics the number of people we survey until we find someone who has taken Statistics the number of sodas students drink per day

the number of people we survey until we find someone who has taken Statistics

Events are equally possible if ... none of them will necessarily happen as a result of a trial there is reason to consider that none of them is more possible (probable) than other there is reason to consider that one of them is more possible (probable) than other at least one of them will necessarily happen as a result of a trial one of them will necessarily happen as a result of a trial

there is reason to consider that none of them is more possible (probable) than other

Given following joint probability distribution table. Find whether X and Y are independent Dependent, as their product of marginal densities equal joint density for every possible pair (x,y) Dependent, the product of the marginal densities does not equal the joint density for every possible pair (x,y) Independent, as their product of marginal densities equal joint density for every possible pair (x,y) Cannot determine 0

Dependent, the product of the marginal densities does not equal the joint density for every possible pair (x,y)

Two events are said to be independent if the occurrence of one event: Means that the second event cannot occur Does not affect the probability of the occurrence of the other event Means that the second event is certain to occur No right answer Means that the first event is certain to occur

Does not affect the probability of the occurrence of the other event