Expected values of random variables

Learning Objectives Explain that an 'expected value' is a prediction we can calculate. Find a common denominator for two fractions with unlike denominators. Convert fractions into equivalent fractions with a common denominator. Add two fractions with unlike denominators to find a total 'expected value'. Subtract two fractions with unlike denominators to compare 'expected values'. Solve word problems about game outcomes using fraction addition and subtraction. If you spin a prize wheel that gives you 1/2 of a pizza and another that gives 1/3 of a pizza, what total fraction of a pizza would you expect to get? 🍕 In this lesson, we will learn how to predict outcomes, which we'll call 'expected values'. We will do this by learning a...

TermDefinitionExample Random VariableIn our games, this is a 'mystery value' or a prize you can win. It's a variable because the prize can change each time you play.The prize from a spinner could be 1/2 a candy bar or 1/4 of a candy bar. The fraction you land on is the random variable. Expected ValueA smart guess or prediction of a total outcome. For our lesson, we find this by adding or subtracting the fraction values from our game.If one game gives you 1/2 a point and another gives 1/4 of a point, the expected total value is 1/2 + 1/4 = 3/4 of a point. Unlike DenominatorsThis is when two fractions have different bottom numbers. The denominator tells us how many equal parts the whole is split into.The fractions 1/3 and 1/4 have unlike denominators because 3 and 4 are diffe...

Rule for Finding a Common Denominator To find a common denominator for a/b and c/d, find a common multiple of b and d. A simple way is to multiply them: b * d. Use this as the first step before you can add or subtract fractions with different bottom numbers. This makes sure you are adding parts of the same size. Formula for Adding with Unlike Denominators a/b + c/d = (a*d)/(b*d) + (c*b)/(d*b) First, convert each fraction to an equivalent fraction with the new common denominator. Then, add the new numerators and keep the common denominator the same. Formula for Subtracting with Unlike Denominators a/b - c/d = (a*d)/(b*d) - (c*b)/(d*b) Just like addition, convert each fraction to have a common denominator. Then, subtract the second numerator from the first and keep the...