Which field heavily utilizes probability to analyze and make predictions from data?
History
Philosophy
Data Science
Literature
If the PDF of a continuous variable is a flat line over a range, what does this imply about the distribution?
It's uniformly distributed.
It's normally distributed.
It's exponentially distributed.
It's a Poisson distribution.
A fair six-sided die is rolled. What is the probability of rolling an even number?
1/6
1/2
1/3
2/3
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?
0.7
1
0.5
0.3
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(aX) = aE(X) for a constant 'a'
E(c) = c for a constant 'c'
E(X²) = [E(X)]²
If a random variable X is multiplied by a constant 'c', how does it affect its expected value?
E(cX) = E(X) + c
E(cX) = c * E(X)
E(cX) = E(X)
E(cX) = E(X) / c
A random variable Y has an expected value of 5 and a variance of 4. What is the expected value of Y - 2?
9
3
7
If the probability of an event happening is 0.3, what is the probability of the event NOT happening?
0.6
What is the probability that a randomly selected person was born on a Tuesday, assuming births are equally likely on any day of the week?
1/365
1/12
1/52
1/7
For a standard normal distribution (mean 0, standard deviation 1), what does the CDF tell you at the value 0?
The most frequent value in the dataset.
The probability density at the exact center of the distribution.
The probability of observing a value less than or equal to 0.
The probability of observing a value of exactly 0.