Expected Value Statistics - Online Math Tutoring

Expected Value Statistics - Online Math Tutoring Definition: - The expected value of a discrete random variable x is the value that is expected to occur per repetition, on average, if an experiment is repeated a large number of times. It is denoted by E(x) and calculated as E(x)= x P(x) The expected value is also known as mean and is denoted by ; that is = x P(x) Example:- Below the probability distribution table where x represents the number of breakdowns for a machine during a given week, and P(x) is the probability of the corresponding value of x x P(x) 0 0.15 1 0.20 2 0.35 3 0.30 To find the expected value of breakdowns per week for this machine, we multiply each value of x by its probability and these products. This sum gives the mean of the probability distribution of x. The products x P(x) are listed in the third column of the below table. The sum of these products give x P(x) which is the expected value of x. Calculating the expected value for the probability distribution of breakdowns. X P(x) x P(x) 0 0.15 0*0.15= 0 1 0.20 1*0.20= 0.20 2 0.35 2*0.35= 0.70 3 0.30 3*0.30= 0.90 x P(x)=1.80 The expected value is E(x)= 1.80