Problem:

The number of mountain bikes sold per day at a local bike dealership in Tagum City, along with its corresponding probabilities, is shown in the succeeding table. Compute the Mean, Variance, and Standard Deviation of the probability distribution by following the steps. Number of Mountain Bikes Sold QX Probability (X) 0 1 2 3 4 Steps Solution 1. Construct the Number of Mountain probability Bikes Sold (X) Probability (X) distribution for the random 0 variable X 1 representing the number of 2 mountain bikes sold. 3 4 2. Multiply the Number of value of the Mountain Bikes Probability (X) X - P(X) random variable Sold (X] X by the O corresponding probability. 2 3 4 3. Add the results Number of obtained in Step Mountain Bikes Probability (X) X . P() 1. Sold (X]0 4 H = EX - F(X) = The mean of the probability distribution is The result says that adding all the probabilities of the random variable (number of mountain bikes) in the probability distribution, the average value that you can have is 4. Subtract the mean from each Number value of the of Probability random variable Mountain (X X - P(X) X - M X. Bikes Sold (X) 0 2 3 4 5. Square the Number obtained result of in Step 4. Mountain Probability X - W (X - H) Bikes Sold (X) 2 36. Miply the results obtained in Step 5 by the corresponding '3". Get the sum of the results obtained in Step 6. The result is the value of the The variance of the probability distribution is The resutt says that the spread or variability of the probability distribution is _ 8. Get the square U=VE(X - #]] . P(X) root of the 35 variance in Step 7to get the standard The standard deviation of the probability deviation. distribution is The result says that there is a distance or deviation of from the mean