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

True

False

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

True

False

6. Which of these is a continuous probability distribution?

Binomial distribution

Poisson distribution

Exponential distribution

Geometric distribution

7. 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

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

0.25

0.5

0.75

1

9. 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

10. 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

11. 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

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

2.5

5

7.5

10

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

P(A) + P(B)

P(A) × P(B)

0

1

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

Mean only

Standard deviation only

Lambda (rate parameter)

Skewness

15. 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

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

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

6. Which of these is a continuous probability distribution?

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

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

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

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

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

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

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

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

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

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

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

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

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

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