ECE302 Quiz-03

What does a probability mass function (PMF) specify?

• The possible values of a random variable
  

• 
  The probability of obtaining a certain value of a random variable

• The cumulative sum of probabilities

• The difference between continuous and discrete variables

What is the key difference between a histogram and a PMF?

• A histogram is ideal, and a PMF is empirical
  

• A PMF is the ideal histogram
  

• A PMF represents frequencies, while a histogram represents probabilities

• Histograms are non-parametric, PMFs are parametric

What condition must a PMF satisfy?

• All probabilities must be greater than zero

• The sum of probabilities across all states must equal 1

• The sum of probabilities must be less than 1

• Probabilities must always sum to infinity

What does a Cumulative Distribution Function (CDF) represent?

• The probability of obtaining a specific value
  

• The sum of probabilities for all values less than or equal to x

• The average value of a random variable

• The variance of a random variable

Which of the following is NOT a property of a valid CDF?

• It is a sequence of increasing steps
  

• F_X(+∞) = 1
  

• F_X(-∞) = -1
  

• At positions where p_X(x) > 0, there is always a jump

How can you obtain the PMF from the CDF for a discrete random variable?

• By differentiating the CDF
  

• By integrating the CDF
  

• By subtracting consecutive CDF values: p_X(x_k) = F_X(x_k) - F_X(x_k-1)
  

• By multiplying consecutive CDF values