Variance and Standard Deviation of Discrete Random Variables PDF

VARIANCE AND STANDARD DEVIATION OF THE DISCRETE RANDOM VARIABLE THE VARIANCE AND STANDARD DEVIATION DESCRIBE THE AMOUNT OF SPREAD, DISPERSION, OR VARIABILITY OF THE ITEMS IN A DISTRIBUTION. HOW CAN WE DESCRIBE THE SPREAD OR DISPERSION IN A PROBABILITY DISTRIBUTION? IN THIS LESSON, YOU WILL LEARN HO...

VARIANCE AND STANDARD DEVIATION OF THE DISCRETE RANDOM VARIABLE THE VARIANCE AND STANDARD DEVIATION DESCRIBE THE AMOUNT OF SPREAD, DISPERSION, OR VARIABILITY OF THE ITEMS IN A DISTRIBUTION. HOW CAN WE DESCRIBE THE SPREAD OR DISPERSION IN A PROBABILITY DISTRIBUTION? IN THIS LESSON, YOU WILL LEARN HOW TO COMPUTE THE VARIANCE AND STANDARD DEVIATION OF A DISCRETE PROBABILITY DISTRIBUTION. Variance and Standard Deviation of a Random Variable The variance and standard deviation are two values that describe how scattered or spread out the scores are from the mean value of the random variable. The variance, denoted as σ², is determined using the formula: σ² = ∑(𝑥 − µ)²p(x) The standard deviation σ is the square root of the variance, thus, σ= σ² - variance µ - mean σ – standard deviation p(x) – probability of the outcome STEPS IN FINDING THE VARIANCE AND STANDARD DEVIATION 1. Find the mean of the probability distribution. 2. Subtract the mean from each value of the random variable X. 3. Square the result obtained in Step 2. 4. Multiply the results obtained in Step 3 by the corresponding probability. 5. Get the sum of the results obtained in Step 4. Results obtained is the value of the variance of probability distribution. To Solve for Standard Deviation: Get the square root of the variance σ² = ∑(𝑥 − µ)²p(x) = 1.56 σ = √1.56 = 1.25 So, the variance of the number of cars sold per day is 1.56 and the standard deviation is 1.25.