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To calculate standard deviation we first need the variance. For continuous random variable with mean value and probability density. 2 Var (X ) E (X - ) 2 From the definition of the variance we can get. Is the mean The symbol ‘’ represents the population mean. Answer (1 of 7): Because if we didn’t square it we would always calculate it as zero. The variance of random variable X is the expected value of squares of difference of X and the expected value. This makes it simply the arithmetic average of the data. In order to select the right project, you need to calculate the expected value of each project and compare the values with each other. In fact, it’s right at the center of every 95 CI. Is expected value always the mean The expectation is the average value or mean of a random variable not a probability distribution. random variables with expected values EXi< and variance Var(Xi)2<. EV the expected value P(X I) the probability of the event X I the event Example of Expected Value (Multiple Events) You are a financial analyst. Random variable X has the following probability function: xĮ( X) = 0 x 0.1 + 1 x 0.2 + 2 x 0.4 + 3 x 0.3Ī bar graph of the probability function, with the expected value labelled, is shown below. STAT1010 Sampling distributions x-bar 11 Interpretation of the 95 Confidence Interval (CI) for a Population Mean 31 We are 95 confident that this interval contains the true parameter value. The expected value is the ‘long-run mean’ in the sense that, if as more and more values of the random variable were collected (by sampling or by repeated trials of a probability activity), the sample mean becomes closer to the expected value.įor a discrete random variable the expected value is calculated by summing the product of the value of the random variable and its associated probability, taken over all of the values of the random variable. The expected value of random variable X is often written as E( X) or µ or µX. The population mean for a random variable and is therefore a measure of centre for the distribution of a random variable.