Probability Theory and Distributions Quiz

1. If P(A) = 0.4 and P(B|A) = 0.6, what is P(A and B)?

0.24

0.4

0.6

1

2. If X and Y are independent random variables, then Var(X + Y) = Var(X) + Var(Y). True or False?

True

False

3. The cumulative distribution function (CDF) of a random variable is always increasing. True or False?

True

False

4. Which parameter determines the shape of the exponential distribution?

Mean only

Standard deviation only

Lambda (rate parameter)

Skewness

Submit

6. If two events are mutually exclusive, what is P(A and B)?

P(A) + P(B)

P(A) × P(B)

0

1

7. The probability density function (PDF) of a continuous distribution must be non-negative. True or False?

True

False

8. In a uniform distribution on [a, b], the expected value is equal to (a + b)/2. True or False?

True

False

9. Which of these is a continuous probability distribution?

Binomial distribution

Poisson distribution

Exponential distribution

Geometric distribution

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11. If P(A) = 0.3 and P(B) = 0.5, and events A and B are independent, what is P(A and B)?

0.15

0.8

0.65

0.35

Submit

13. For a standard normal distribution, what is P(Z < 0)?

0.25

0.5

0.75

1

14. What is the main statement of the Central Limit Theorem?

Sample means are normally distributed regardless of population shape

All populations follow a normal distribution

Variance always equals the mean

Probability distributions must be symmetric

15. Which distribution is used to model the number of successes in a fixed number of independent trials?

Poisson distribution

Binomial distribution

Exponential distribution

Uniform distribution

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17. If X follows a binomial distribution with n = 10 and p = 0.5, what is E(X)?

2.5

5

7.5

10

Submit

19. Which of the following is a property of the normal distribution?

It is always skewed to the right

It is symmetric about its mean

It has a minimum value of zero

It is bounded between 0 and 1

20. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

1/6

1/3

1/2

2/3

DataX Probability Theory and Distributions Quiz

1. If P(A) = 0.4 and P(B|A) = 0.6, what is P(A and B)?

2.

What first name or nickname would you like us to use?

2. If X and Y are independent random variables, then Var(X + Y) = Var(X) + Var(Y). True or False?

3. The cumulative distribution function (CDF) of a random variable is always increasing. True or False?

4. Which parameter determines the shape of the exponential distribution?

5. The number of degrees of freedom in a chi-square distribution depends on the ____.

6. If two events are mutually exclusive, what is P(A and B)?

7. The probability density function (PDF) of a continuous distribution must be non-negative. True or False?

8. In a uniform distribution on [a, b], the expected value is equal to (a + b)/2. True or False?

9. Which of these is a continuous probability distribution?

10. The sum of all probabilities in a probability distribution must equal ____.

11. If P(A) = 0.3 and P(B) = 0.5, and events A and B are independent, what is P(A and B)?

12. The Poisson distribution is often used to model the number of ____ occurring in a fixed time interval.

13. For a standard normal distribution, what is P(Z < 0)?

14. What is the main statement of the Central Limit Theorem?

15. Which distribution is used to model the number of successes in a fixed number of independent trials?

16. The standard deviation of a random variable is the square root of its ____.

17. If X follows a binomial distribution with n = 10 and p = 0.5, what is E(X)?

18. The expected value of a discrete random variable X is also called its ____.

19. Which of the following is a property of the normal distribution?

20. A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?