A random variable X has a probability distribution as follows: P(X=0) = 0.2, P(X=1) = 0.3, P(X=2) = 0.5. What is the expected value of X?
0.5
1
1.2
1.5
A website experiences an average of 5 user registrations per hour. What distribution best models the number of registrations in a given hour?
Uniform Distribution
Poisson Distribution
Geometric Distribution
Binomial Distribution
A random variable X follows a uniform distribution between 0 and 10. What is the probability that X is greater than 7?
0.1
0.7
0.3
0.2
A random variable Y has an expected value of 5 and a variance of 4. What is the expected value of Y - 2?
3
7
9
Which of the following is an example of a discrete random variable?
The weight of an apple.
The height of a student.
The number of heads when a coin is flipped four times.
The temperature of a room.
A random number generator produces a uniform distribution between 0 and 1. What is the probability that the generated number is greater than 0.7?
A bag contains 4 red balls and 6 blue balls. You draw two balls out of the bag without replacement. What is the probability that both balls are red?
4/25
8/15
1/3
2/15
If a constant value 'c' is added to every observation of a data set, what happens to the variance?
Increases by 'c²'
Increases by 'c'
Decreases by 'c'
Remains unchanged
Which of the following is NOT a property of a Cumulative Distribution Function (CDF)?
It represents the area under the PDF curve.
It ranges between 0 and 1.
It is only defined for discrete random variables.
It is always non-decreasing.
If two events are mutually exclusive, what is the probability that both events occur?
Cannot be determined
0