If a random variable X represents the number of tails in two coin flips, what is P(X = 1) using its Probability Mass Function (PMF)?
0.75
0.25
0.50
1.00
What does the expected value (mean) of a random variable represent?
The spread or dispersion of the variable's values.
The most frequent value the variable takes on.
The probability of the variable taking on a specific value.
The average of all possible values, weighted by their probabilities.
A website experiences an average of 5 user registrations per hour. What is the probability that there will be exactly 3 registrations in the next hour?
This can be approximated by a binomial distribution.
This can be approximated by a uniform distribution.
This scenario does not fit the distributions described.
This can be approximated by a geometric distribution.
Which of the following is NOT a property of expected value?
E(X + Y) = E(X) + E(Y) for random variables X and Y
E(c) = c for a constant 'c'
E(aX) = aE(X) for a constant 'a'
E(X²) = [E(X)]²
If two events are mutually exclusive, what is the probability that both events occur?
0.5
Cannot be determined
0
1
In a lottery, 1000 tickets are sold and there is one winning ticket. If you buy one ticket, what is the probability of winning?
0.1
0.001
0.01
Which of the following is an example of a discrete random variable?
The weight of an apple.
The temperature of a room.
The height of a student.
The number of heads when a coin is flipped four times.
If a random variable X follows a standard normal distribution, what is P(X = 0)?
Cannot be determined.
You are playing a game where you roll a die until you get a 6. What is the probability that it takes you exactly 4 rolls?
(1/6)^4
(5/6)^4
(5/6)^3 * (1/6)
(1/6)^3 * (5/6)
A fair six-sided die is rolled. What is the probability of rolling an even number?
1/3
1/6
2/3
1/2