ABM A – Unit 6- Set 3 – Motivational Banker

1. For a discrete random variable, what does the probability distribution list?

Only the possible values

Only the probabilities

The possible values and their probabilities

The average value

Question 1 of 50

2. What type of function is used to describe the probability distribution of a continuous random variable?

Cumulative distribution function

Probability density function

Joint probability function

Marginal probability function

Question 2 of 50

3. How is a probability distribution often represented for a discrete random variable?

As a curve

As a line

As a table

As a point

Question 3 of 50

4. For a continuous random variable, what does the probability distribution provide?

Only the possible values

Only the probabilities

The range of values and their probabilities

The expected value

Question 4 of 50

5. What information does a probability distribution of a random variable convey?

Only the average value

Only the standard deviation

Probabilities of all possible values

Only the most likely outcome

Question 5 of 50

6. What is the probability distribution for a discrete random variable often presented as?

A graph

A formula

A cumulative distribution

A table

Question 6 of 50

7. What term is used for the function that gives the probability of a continuous random variable being within a certain range of values?

Cumulative distribution function

Probability density function

Joint probability function

Marginal probability function

Question 7 of 50

8. What does PMF stand for in probability?

Probability Mass Factor

Probability Mass Function

Probability Maximum Function

Probability Measurement Factor

Question 8 of 50

9. What type of random variable does a PMF apply to?

Only continuous random variables

Only discrete random variables

Both continuous and discrete random variables

Neither continuous nor discrete random variables

Question 9 of 50

10. What does a probability mass function (PMF) give the probability of?

Only the average value

Only the most likely outcome

Each possible outcome of a discrete random variable

Only the range of values

Question 10 of 50

11. How is the PMF defined for a discrete random variable?

P(X = x) = p(x)

P(X = x) = x

P(X = p(x))

P(x) = X

Question 11 of 50

12. In the PMF equation P(X = x) = p(x), what does P(X = x) represent?

Probability that X is equal to x

Probability that X is not equal to x

Average value of X

Range of X

Question 12 of 50

13. What does p(x) represent in the PMF equation?

The probability that X is equal to x

The average value of X

The range of X

The probability that X is not equal to x

Question 13 of 50

14. What does a PMF assign probabilities to?

Only a few outcomes

Only the most extreme outcomes

Only impossible outcomes

Each possible outcome of a discrete random variable

Question 14 of 50

15. Which type of random variable does a PMF not apply to?

Continuous random variables

Discrete random variables

Both continuous and discrete random variables

Neither continuous nor discrete random variables

Question 15 of 50

16. What information does a PMF provide for each possible outcome of a discrete random variable?

Only the probability of occurrence

Only the frequency of occurrence

Both the probability and frequency of occurrence

Only the average value

Question 16 of 50

17. How does the PMF differ from other probability functions?

It applies only to continuous random variables

It assigns probabilities to discrete outcomes

It is defined as the average value of a random variable

It is unrelated to probability

Question 17 of 50

18. What does PDF stand for in probability?

Probability Distribution Factor

Probability Density Function

Probability Distribution Function

Probability Determination Function

Question 18 of 50

19. What type of probability distribution does a PDF describe?

Only discrete probability distributions

Only continuous probability distributions

Both discrete and continuous probability distributions

Neither discrete nor continuous probability distributions

Question 19 of 50

20. What does a PDF give the relative likelihood of?

Only the most extreme outcomes

Only the average outcome

Each possible outcome of a discrete random variable

The random variable taking a specific value for continuous distributions

Question 20 of 50

21. How is the PDF defined for a continuous random variable?

f(x) = dF(x)/dx

f(x) = F(x)

f(x) = 1/F(x)

f(x) = 1/dF(x)/dx

Question 21 of 50

22. In the PDF equation f(x) = dF(x)/dx, what does f(x) represent?

The cumulative distribution function

The probability that X is equal to x

The probability density function

The average value of X

Question 22 of 50

23. What is F(x) in the PDF equation?

The probability density function

The random variable X

The cumulative distribution function

The average value of X

Question 23 of 50

24. What does dF(x)/dx represent in the PDF equation?

The probability density function

The average value of X

The derivative of the cumulative distribution function

The range of X

Question 24 of 50

25. How does the PDF differ from the PMF?

PDF is for discrete random variables, PMF is for continuous random variables

PDF assigns probabilities to discrete outcomes, PMF assigns probabilities to continuous outcomes

PDF is for continuous random variables, PMF is for discrete random variables

PDF is unrelated to probability, PMF is related to probability

Question 25 of 50

26. What information does the PDF provide for a continuous random variable?

Only the probability of occurrence

Only the frequency of occurrence

The relative likelihood of taking specific values

Only the average value

Question 26 of 50

27. What does the area under the curve of the PDF between two values of x represent?

The average value of the random variable

The probability that the random variable takes a value within that interval

The cumulative distribution function

The range of the random variable

Question 27 of 50

28. What does the binomial distribution describe?

The average value of a random variable

The number of successful outcomes in independent trials

The probability density function for continuous random variables

The cumulative distribution function for discrete random variables

Question 28 of 50

29. In what situations is the binomial distribution used?

Situations with only one possible outcome

Situations with exactly three possible outcomes

Situations with two possible outcomes, such as success or failure

Situations with an infinite number of possible outcomes

Question 29 of 50

30. How is the binomial distribution defined?

By the number of trials (p) and the probability of success in each trial (n)

By the average value and variance

By the mean and standard deviation

By the number of trials (n) and the probability of success in each trial (p)

Question 30 of 50

31. What does the binomial probability formula P(k) = (n choose k) * p^k * (1 - p)^(n-k) calculate?

The cumulative distribution function

The probability of success in each trial

The average value of the distribution

The probability of getting exactly k successes in n trials

Question 31 of 50

32. What does (n choose k) represent in the binomial probability formula?

The cumulative distribution function

The probability density function

The mean of the distribution

The binomial coefficient

Question 32 of 50

33. How are the mean and variance of the binomial distribution calculated?

Mean = p, Variance = p^2

Mean = n + p, Variance = n * p

Mean = n * p, Variance = n * p * (1-p)

Mean = n * (1-p), Variance = n * p

Question 33 of 50

34. In the binomial distribution, what does "n*p" represent?

The probability of success in each trial

The cumulative distribution function

The mean of the distribution

The number of trials

Question 34 of 50

35. What does the binomial distribution model in situations with two possible outcomes?

Situations with only one possible outcome

Situations with an infinite number of possible outcomes

Situations with exactly three possible outcomes

Situations with success or failure, heads or tails, or yes or no

Question 35 of 50

36. What applications does the binomial distribution have?

Applications only in statistics

Applications only in economics

Applications only in engineering

Applications in statistics, economics, engineering, and biology

Question 36 of 50

37. What parameters define the binomial distribution?

The mean and variance

The number of trials (n) and probability of success in each trial (p)

The cumulative distribution function

The average value and variance

Question 37 of 50

38. What does the Poisson distribution model?

The average value of a random variable

The number of successes in independent trials

The number of occurrences of a specific event in a fixed interval

The cumulative distribution function for continuous random variables

Question 38 of 50

39. Who is the Poisson distribution named after?

Isaac Newton

Albert Einstein

Simeon Denis Poisson

Blaise Pascal

Question 39 of 50

40. What parameter characterizes the Poisson distribution?

The mean and variance

The standard deviation

The probability of success in each trial

The average rate of occurrences (?)

Question 40 of 50

41. What does the probability mass function (PMF) of the Poisson distribution calculate?

The cumulative distribution function

The probability of success in each trial

The relative likelihood of taking specific values

The probability of the random variable taking a specific value

Question 41 of 50

42. What does e represent in the PMF of the Poisson distribution?

The cumulative distribution function

The average value of the distribution

The mathematical constant approximately equal to 2.71828

The standard deviation

Question 42 of 50

43. In the Poisson distribution, what does X represent?

The mean of the distribution

The random variable representing the number of occurrences of the event

The cumulative distribution function

The average rate of occurrences

Question 43 of 50

44. What does k! represent in the PMF of the Poisson distribution?

The cumulative distribution function

The average value of the distribution

The factorial of k

The standard deviation

Question 44 of 50

45. What does the average rate of occurrences (?) represent in the Poisson distribution?

The probability of success in each trial

The mean and variance

The standard deviation

The average number of occurrences in a fixed interval

Question 45 of 50

46. How is the Poisson distribution used in an example?

Modeling the average value of a random variable

Modeling the number of occurrences of a specific event in a fixed interval

Modeling the cumulative distribution function

Modeling the probability of success in each trial

Question 46 of 50

47. What does the probability P(X=3) represent in the Poisson distribution example?

The cumulative distribution function

The average value of the distribution

The probability of receiving exactly 3 complaints in a day

The probability of success in each trial

Question 47 of 50

48. What is another name for the Normal Distribution?

Binomial Distribution

Exponential Distribution

Gaussian Distribution

Poisson Distribution

Question 48 of 50

49. What does the bell-shaped curve of the Normal Distribution indicate?

Skewness

Symmetry around the mean

Kurtosis

Discreteness

Question 49 of 50

50. What characterizes the Normal Distribution?

A skewed curve

A uniform curve

A bell-shaped curve

A step-like curve

Question 50 of 50

ABM A – Unit 6- Set 3

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