MFSC_Quize_1

What is the key difference between a probability mass function (PMF) and a probability density function (PDF)?

• PMF applies to continuous variables, and PDF applies to discrete variables.

• PMF applies to discrete variables, and PDF applies to continuous variables.

• Both PMF and PDF apply to continuous variables.

• Both PMF and PDF apply to discrete variables.

What is the CDF of a continuous random variable X defined as?

• P ( X = x )

• P ( X ≥ x )

• P ( X > x )

• P ( X ≤ x)

Which of the following is a parametric family of distributions?

• Binomial distribution

• Normal distribution

• Poisson distribution

• All of the above

The expected value of a discrete random variable X is given by:

• ∑ P ( X = x) . x

• ∑ P ( X = x) . x²

• ∫P ( X = x) . xdx

• ∫P ( X = x) . x²dx

The variance of a random variable X is:

• E ( X )

• E ( X² )

• E [ ( X− E ( X ) )²]

• E(X²)−[E(X)]²

If X and Y are two random variables, the conditional expectation of X given Y = y is denoted by:

• • E ( X ∣ Y = y )

• P ( X = x ∣ Y = y )

• ∫ P ( X ∣ Y = y ) dx

• ∑ P ( X ∣ Y = y ) ⋅ X

According to the Central Limit Theorem, the sum of a large number of independent and identically distributed random variables approaches

• A binomial distribution

• A Poisson distribution

• A normal distribution

• A uniform distribution

The multivariate Central Limit Theorem states that the distribution of the sum of multivariate random variables approaches:

• A multivariate Poisson distribution

• A multivariate normal distribution

• A uniform distribution

• A binomial distribution

Which of the following is an example of a probabilistic inequality?

• Chebyshev’s inequality

• Markov’s inequality

• Jensen’s inequality

• All of the above

In a Markov chain, the future state depends on:

• The present state and the previous state

• The entire history of states

• Only the present state

• Both present and future states