Expected Value and Standard Deviation

Calculate the standard deviation given the distribution in the picture;

The function in the given table is a probability function of a discrete random variable 𝑋. Find the standard deviation of 𝑋. Give your answer to two decimal places.

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14

• 4.67

• 5

• 7.5

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

• $12.50

• $5

• $7.50

• $10

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

• 220

• 239

• 261

• 309

• 320

• $55

• $65

• $75

• $85

• $2.50

• $5

• -$2.50

• $0

Data was compiled and the number of goals for a hockey team per game and the corresponding probabilities are given below. If this hockey team plays an 82-game season, what is the expected cumulative goal total for the next season?

• 220

• 239

• 261

• 309

• 320

The distribution describes lotto ticket probabilities to win different amounts. What is the expected value for this lotto ticket? (Do not include a dollar symbol in answer)

Mathematical Equivalence

ON

Answer explanation

Expected Value is calculated by adding the product each paired outcome and probability

A quiz game has three questions. Each correct answer scores 5 points, and each wrong answer scores 0 points. If a player guesses all answers, assuming a 50% chance of getting each question right, what is the expected score?

• 7.5

• 10

• 12.5

• 15