Which of the following measures the spread or dispersion of a random variable's values around its expected value?
Expected Value
Probability Mass Function
Cumulative Distribution Function
Variance
A basketball player makes 80% of his free throws. What is the probability that he makes his next two free throws?
0.64
0.80
0.96
0.40
A fair coin is flipped 5 times. What is the probability of getting exactly 3 heads?
1/2
1/8
3/16
5/16
In a standard deck of 52 cards, you draw one card. What is the probability of drawing a heart or a spade?
1/13
1/4
1/52
Suppose you are playing a game where you flip a coin until you get heads. What is the probability that it takes exactly 4 flips to get the first heads?
1/16
Which of the following is NOT a property of expected value?
E(aX) = aE(X) for a constant 'a'
E(X + Y) = E(X) + E(Y) for random variables X and Y
E(X²) = [E(X)]²
E(c) = c for a constant 'c'
What does the complement rule in probability state?
The probability of an event not happening is 1 minus the probability of it happening.
The probability of an event happening is equal to the probability of it not happening.
The probability of two events happening is the sum of their individual probabilities.
The probability of an event is always 1.
How is a random variable different from a regular variable in programming?
There's no difference, both terms are interchangeable.
Random variables have an associated probability distribution.
Regular variables cannot be used in statistical analysis.
Random variables can only store numeric data.
If a random variable X follows a standard normal distribution, what is P(X = 0)?
0
1
Cannot be determined.
0.5
A website experiences an average of 5 user registrations per hour. What distribution best models the number of registrations in a given hour?
Binomial Distribution
Uniform Distribution
Geometric Distribution
Poisson Distribution