Front

What is Expected Value?

Back

The Expected Value (EV) is a calculated average of all possible outcomes of a random variable, weighted by their probabilities. It represents the long-term average if the experiment were repeated many times.

Tags

CCSS.HSS.MD.A.2

Front

How do you calculate Expected Value?

Back

To calculate the Expected Value, multiply each possible outcome by its probability and then sum all these products. Formula: EV = Σ (X * P(X)) where X is the outcome and P(X) is the probability.

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of a random variable with outcomes 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively?

Back

EV = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 5 + 6 + 3 = 14.

Tags

CCSS.HSS.MD.A.2

Front

In a community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. What is the expected number of children?

Back

EV = (1 * 0.3) + (2 * 0.43) + (3 * 0.27) = 0.3 + 0.86 + 0.81 = 1.97.

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of a stock with a 40% chance of being worth $50, a 35% chance of $60, and a 25% chance of $70?

Back

EV = (50 * 0.4) + (60 * 0.35) + (70 * 0.25) = 20 + 21 + 17.5 = 58.5.

Tags

CCSS.HSS.MD.A.2

Front

What is the mean (expected value) of a probability distribution?

Back

The mean (expected value) is the average of all possible values of a random variable, weighted by their probabilities.

Tags

CCSS.HSS.MD.A.2

Front

What is the formula for calculating the mean of a discrete probability distribution?

Back

Mean = Σ (X * P(X)), where X is each outcome and P(X) is the probability of that outcome.

Tags

CCSS.HSS.MD.A.2

Front

What is the probability of getting exactly 6 heads in 10 tosses of a fair coin?

Back

Using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k). For 6 heads: P(6) = (10 choose 6) * (0.5)^6 * (0.5)^4 = 0.205.

Front

What does 'n choose k' mean in probability?

Back

'n choose k' (denoted as C(n, k) or nCk) is the number of ways to choose k successes in n trials, calculated as n! / (k!(n-k)!).

Front

What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4