expected value

Examples of expected value in the following topics:

• Expected Values of Discrete Random Variables

  • The expected value of a random variable is the weighted average of all possible values that this random variable can take on.
  • In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) of a random variable is the weighted average of all possible values that this random variable can take on.
  • The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), as is also the case with the sample mean.
  • This is intuitive: the expected value of a random variable is the average of all values it can take; thus the expected value is what one expects to happen on average.
  • The intuition, however, remains the same: the expected value of $X$ is what one expects to happen on average.

• Expected Value and Standard Error

  • In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) of a random variable is the weighted average of all possible values that this random variable can take on.
  • The expected value may be intuitively understood by the law of large numbers: the expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity.
  • The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), as is also the case with the sample mean.
  • If we were to selected one number from the box, the expected value would be:
  • The new expected value of the sum of the numbers can be calculated by the number of draws multiplied by the expected value of the box: $25\cdot 2.2 = 55$.

• Expected Value

  • The expected value is a weighted average of all possible values in a data set.
  • In probability theory, the expected value refers, intuitively, to the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained.
  • More formally, the expected value is a weighted average of all possible values.
  • The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), as is also the case with the sample mean.
  • The expected value plays important roles in a variety of contexts.

• The Correction Factor

  • The expected value is a weighted average of all possible values in a data set.
  • In probability theory, the expected value refers, intuitively, to the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained.
  • More formally, the expected value is a weighted average of all possible values.
  • The value may not be expected in the ordinary sense—the "expected value" itself may be unlikely or even impossible (such as having 2.5 children), as is also the case with the sample mean.
  • The expected value plays important roles in a variety of contexts.

• Mean or Expected Value and Standard Deviation

  • The expected value is often referred to as the "long-term"average or mean .
  • The expected value is 1.1.
  • The expected value is the expected number of times a newborn wakes its mother after midnight.
  • Add the last column to find the expected value. µ = Expected Value = 105/50 = 2.1
  • What is the expected value, µ?

• Plotting the Residuals

  • The residual plot illustrates how far away each of the values on the graph is from the expected value (the value on the line).
  • The expected value, being the mean of the entire population, is typically unobservable, and hence the statistical error cannot be observed either.
  • The residual plot illustrates how far away each of the values on the graph is from the expected value (the value on the line).
  • So, based on the linear regression model, for a 2006 value of 415 drunk driving fatalities we would expect the number of drunk driving fatalities in 2009 to be lower than 377.
  • So, based on the linear regression model, for a 2006 value of 439 drunk driving fatalities we would expect the number of drunk driving fatalities for 2009 to be higher than 313.

• Discounted Cash Flow Approach

  • The discounted cash flow approach finds the value of an asset using its expected return and the present values of future cash flows.
  • An asset is expected to return $1,000 each year for a period of 5 years.
  • In the DCF approach, all future-expected positive and negative cash flows associated with the asset are discounted using the appropriate interest rate (such as the expected return found using CAPM).
  • These present values are summed to give the net present value (NPV) of the asset.
  • -- Use this equation to find the present value of a future terminal value.

• Present Value of Payments

  • The value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
  • As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate.
  • Therefore, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.
  • The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments.
  • Bond price is the present value of coupon payments and face value paid at maturity.

• Expected Dividends, No Growth

  • A no-growth company would be expected to return high dividends under traditional finance theory.
  • At the other end of the spectrum, investors of a "no growth," or value stock will expect the firm to retain little cash for investment, and to distribute a comparatively greater proportion to investors as a dividend.
  • No growth, high dividend stocks may appeal to value investors.
  • Thus, high dividends and low reinvestment of retained earnings can signal an appealing value stock to an investor.
  • Describe how a company should make a dividend decision when it expect no growth

• Expectancy Theory

  • Vroom introduces three variables within his expectancy theory: valence (V), expectancy (E), and instrumentality (I).
  • These three elements also have clearly defined relationships: effort-performance expectancy (E>P expectancy), performance-outcome expectancy (P>O expectancy).
  • These three components of expectancy theory (expectancy, instrumentality, and valence) fit together in this fashion:
  • V(O): Valence is the value individuals place on outcomes (O) based on their needs, goals, values, and sources of motivation.
  • Factors associated with the individual's valence are values, needs, goals, preferences, sources of motivation, and the strength of an individual's preference for a particular outcome.