Expected Value (Leaving Cert Mathematics): Quizzes

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Expected Value
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What does the expected value represent in probability and statistics?

Long-term average over many trials

What statistical measure does expected value provide?

Central tendency

What is the formula for expected value of a discrete random variable?

E(X)=∑(x×P(x))E(X) = \sum (x \times P(x))

In the discrete EV formula, what does P(x)P(x) represent?

Probability of xx

In the continuous EV formula, what does f(x)f(x) represent?

Probability density function

Does the expected value necessarily equal one of the possible outcomes?

No, it represents average over trials

When is a game considered 'fair' in terms of expected value?

When EV equals zero

In which fields is EV used to evaluate risks and returns?

Economics, insurance, gambling

What is the probability of each outcome when rolling a fair six-sided die?

16\frac{1}{6}

What is the expected value when rolling a fair six-sided die?

3.53.5

A biased coin has 70% chance of heads (value 1) and 30% tails (value 0). Which setup is correct?

P(Heads)=0.7,P(Tails)=0.3P(\text{Heads}) = 0.7, P(\text{Tails}) = 0.3

What is the EV for a biased coin with 70% heads (value 1) and 30% tails (value 0)?

0.70.7

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Fundamentals of Probability

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Expected Value

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Expected Value

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Expected Value

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Fundamentals of Probability

The Basics of Counting

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Combinations

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Events

Expected Value

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Expected Value

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Probability

The Basics of Counting

Permutations / Arrangements

The Basics of Probability

Combinations

Set Theory and Probability

Combined Events/Bernouilli Trials

Events

Expected Value

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Expected Value

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