The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. \[\begin{array} { | c | c | } \hline x & P [ X ] \\ \hline - 3 & \\ \hline - 2 & \\ \hline 0 & \\ \hline 1 & \\ \hline 2 & \\ \hline \end{array}\] Which of the following statements is correct ?

A) The expected value of $X$ can only be 0 . B) The expected value of $X$ could be 3 . C) The expected value of $X$ could be $0.5$ D) None of these choices are correct A) The expected value of $X$ can only be 0 . B) The expected value of $X$ could be 3 . C) The expected value of $X$ could be $0.5$ D) None of these choices are correct

If X and Y are random variables with E(X) =7 and E(Y) = 3, then E(2X + 3Y) is: \[\begin{array} { | l | l | } \hline \text { A. } & 10 . \\ \hline \text { B. } & 23 . \\ \hline \text { C. } & 27 . \\ \hline \text { D. } & 21 . \\ \hline \end{array}\]

The answer of If X and Y are random variables...

Let X and Y be two independent random variables with the following probability distributions: \[\begin{array}{l} \begin{array} { l | r r r } x & 1 & 2 & 3 \\ \hline p ( x ) & 0.2 & 0.5 & 0.3 \end{array}\\ \begin{array} { l | r r r } y & - 1 & 0 & 1 \\ \hline p ( y ) & 0.3 & 0.3 & 0.4 \end{array} \end{array}\] a. Find the probability distribution of the random variable XY. b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.

a. \[\begin{array} { l | r r r r r r r }

Exam 7: Random Variables and Discrete Probability Distributions

The number of arrivals at a local petrol station between 3:00 and 5:00pm has a Poisson distribution with a mean of 12. a. Find the probability that the number of arrivals between 3:00 and 5:00pm is at least 10. b. Find the probability that the number of arrivals between 3:30 and 4:00pm is at least 10. c. Find the probability that the number of arrivals between 4:00 and 5:00pm is exactly two.

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Question 21

The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. x P[X] -3 -2 0 1 2 Which of the following statements is correct ?

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Question 22

The Poisson random variable is a:

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Question 23

Suppose that customers arrive at a drive-through window at an average rate of three customers per minute and that their arrival follows the Poisson model. a. Write the probability density function of the distribution of the time that will elapse before the next customer arrives. b. Use the appropriate exponential distribution to find the probability that the next customer will arrive within 1.5 minutes. c. Use the appropriate exponential distribution to find the probability that the next customer will not arrive within the next 2 minutes. d. Use the appropriate Poisson distribution to answer part (c).

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Question 24

An advertising executive receives an average of 10 telephone calls each afternoon between 2 and 4pm. The calls occur randomly and independently of one another. a. Find the probability that the executive will receive 13 calls between 2 and 4pm on a particular afternoon. b. Find the probability that the executive will receive seven calls between 2 and 3pm on a particular afternoon. c. Find the probability that the executive will receive at least five calls between 2 and 4pm on a particular afternoon.

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Question 25

A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is:

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Question 26

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of: A. x-0.5 B. x+0.5. C. x-1. D. x+1.

(Short Answer)

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Question 27

For each of the following random variables, indicate whether the variable is discrete or continuous, and specify the possible values that it can assume. a. X = The number of animals visited by a veterinarian in one day. b. X = Closing share price of a particular stock over one month. c. X = The weights of new members at a gymnasium. d. X = The number of students attending a lecture, where the theatre seats 250 people. e. X = The temperature at a seaside resort in the summer.

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Question 28

If X and Y are random variables with E(X) =7 and E(Y) = 3, then E(2X + 3Y) is: A. 10. B. 23. C. 27. D. 21.

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Question 29

Historical data collected at the Commonwealth Bank in Sydney revealed that 80% of all customers applying for a loan are accepted. Suppose that 50 new loan applications are selected at random. a. Find the expected value and the standard deviation of the number of loans that will be accepted by the bank. b. What is the probability that at least 42 loans will be accepted? c. What is the probability that the number of loans rejected is between 10 and 15, inclusive?

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Question 30

Which of the following cannot generate a Poisson distribution?

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Question 31

If X and Y are any random variables with E(X)= 3, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the relationship between X and Y is a: Hint: corr(X,Y) =( E(xy) - E(x)E(y))/

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Question 32

Which of the following best describes a discrete random variable?

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Question 33

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.

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Question 34

Which of the following is not a characteristic of a binomial experiment?

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Question 35

Let X and Y be two independent random variables with the following probability distributions: x 1 2 3 p(x) 0.2 0.5 0.3 y -1 0 1 p(y) 0.3 0.3 0.4 a. Find the probability distribution of the random variable XY. b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.

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Question 36

Which of the following best describes a function that assigns a numerical value to each simple event in a sample space?

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Question 37

The expected value, E(X), of a binomial probability distribution is:

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Question 38

Let X represent the number of computers in an Australian household, for those that own a computer. x 1 2 3 4 5 p(x) .25 .33 .17 .15 .10 a. Find and interpret the expected number of computers in a randomly selected Australian household. b. Find the variance of the number of computers in a randomly selected Australian household.

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Question 39

The number of people winning a lottery ticket each week is an example of a Poisson variable.

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Question 40

Showing 21 - 40 of 55

The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. x P[X] -3 -2 0 1 2 Which of the following statements is correct ?

The Poisson random variable is a:

A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is:

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of: A. x-0.5 B. x+0.5. C. x-1. D. x+1.

If X and Y are random variables with E(X) =7 and E(Y) = 3, then E(2X + 3Y) is: A. 10. B. 23. C. 27. D. 21.

Which of the following cannot generate a Poisson distribution?

If X and Y are any random variables with E(X)= 3, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the relationship between X and Y is a: Hint: corr(X,Y) =( E(xy) - E(x)E(y))/

Which of the following best describes a discrete random variable?

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.

Which of the following is not a characteristic of a binomial experiment?

Let X and Y be two independent random variables with the following probability distributions: x 1 2 3 p(x) 0.2 0.5 0.3 y -1 0 1 p(y) 0.3 0.3 0.4 a. Find the probability distribution of the random variable XY. b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.

Which of the following best describes a function that assigns a numerical value to each simple event in a sample space?

The expected value, E(X), of a binomial probability distribution is:

The number of people winning a lottery ticket each week is an example of a Poisson variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 7: Random Variables and Discrete Probability Distributions

The following table is a valid probability distribution, for a random variable X, where the individual probabilities are unknown. x P[X] -3 -2 0 1 2 Which of the following statements is correct ?

The Poisson random variable is a:

A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is:

Given that X is a binomial random variable, the binomial probability P(X ≥\geq≥ x) is approximated by the area under a normal curve to the right of: A. x-0.5 B. x+0.5. C. x-1. D. x+1.

If X and Y are random variables with E(X) =7 and E(Y) = 3, then E(2X + 3Y) is: A. 10. B. 23. C. 27. D. 21.

Which of the following cannot generate a Poisson distribution?

If X and Y are any random variables with E(X)= 3, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the relationship between X and Y is a: Hint: corr(X,Y) =( E(xy) - E(x)E(y))/

Which of the following best describes a discrete random variable?

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X ≥\geq≥ 9. c. X ≤\leq≤ 10.

Which of the following is not a characteristic of a binomial experiment?

Let X and Y be two independent random variables with the following probability distributions: x 1 2 3 p(x) 0.2 0.5 0.3 y -1 0 1 p(y) 0.3 0.3 0.4 a. Find the probability distribution of the random variable XY. b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.

Which of the following best describes a function that assigns a numerical value to each simple event in a sample space?

The expected value, E(X), of a binomial probability distribution is:

The number of people winning a lottery ticket each week is an example of a Poisson variable.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Continuous Probability Distributions

Statistical Inference: Introduction

Sampling Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Given that X is a binomial random variable, the binomial probability P(X $\geq$ x) is approximated by the area under a normal curve to the right of: A. x-0.5 B. x+0.5. C. x-1. D. x+1.

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations. a. X = 6. b. X $\geq$ 9. c. X $\leq$ 10.