If X is a Continuous Uniform Random Variable on the interval [2, 10], what is the Probability Density Function (PDF) f(x) for x in [2, 10]?
PDF of Uniform[a, b] is f(x) = 1 / (b - a) = 1 / (10 - 2) = 1 / 8 = 0.125.
If events A and B are INDEPENDENT with P(A) = 0.4 and P(B) = 0.5, what is P(A U B)?
$P(A n B) = P(A) * P(B) = 0.4 * 0.5 = 0.2. P(A U B) = P(A) + P(B) - P(A n B) = 0.4 + 0.5 - 0.2 = 0.7.$
Let X be an Exponentially distributed random variable with rate parameter $\lambda = 0.5$. What is the EXPECTED VALUE E[X]?
For Exponential distribution with parameter $\lambda , Mean E[X] = 1 / \lambda = 1 / 0.5 = 2$.
Which of the following statements are TRUE regarding Eigenvalues and Matrix properties? (Select all that apply)
All four statements are fundamental and classical theorems in Linear Algebra.
Consider a random variable X representing the outcome of rolling a fair 6-sided die. What is the expected value E[X]?
$E[X] = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5.$