Mean and Variance of Discrete Random Variable PDF

Mean and Variance of Discrete Random Variable Mean of a Discrete Random Variable The Mean µ of a discrete random variable is the central value or average of its corresponding probability mass function. It is also called as the Expected Value. It is computed using the fo...

Mean and Variance of Discrete Random Variable Mean of a Discrete Random Variable The Mean µ of a discrete random variable is the central value or average of its corresponding probability mass function. It is also called as the Expected Value. It is computed using the formula: µ = ∑ 𝑋𝑃(𝑥) Where x is the outcome and p(x) is the probability of the outcome.  1. Determine the mean or Expected Value of random variable below. Solution: µ = ∑ ⟮𝑥𝑃(𝑥)⟯ = ∑ ⟮0( 1 5 ) + 1( 1 5 ) + 2( 1 5 ) + 3( 1 5 ) + 4(1 5 )⟯ = ∑ ⟮0 + 1 5 + 2 5 + 3 5 + 4 5 ⟯ = 10 5 or 2 Therefore, mean is 2 for the above random variable. The probabilities that a customer will buy 1, 2, 3, 4, or 5 items in a grocery store are 3 10 , 1 10 , 1 10 , 2 10 , and 3 10 , respectively. What is the average number of items that a customer will buy? What is It To solve the above problem, we will follow 3 steps below.  STEPS IN FINDING THE MEAN Step 1: Construct the probability distribution for the random variable X representing the number of items that the customer will buy. Step 2: Multiply the value of the random variable X by the corresponding probability. Step 3: Add the results obtained in Step 2. Results obtained is the mean of the probability distribution. So, the mean of the probability distribution is 3.1. This implies that the average number of items that the customer will buy is 3.1.