Probability Trees and Conditional Expectations

What is the expected value of a random variable defined as?

Given a random variable X with outcomes 10 percent, 20 percent, and 30 percent, and probabilities 0.2, 0.5, and 0.3 respectively, what is the expected value?

Which of the following statements about variance is correct?

If the variance of a random variable is 25, what is the standard deviation?

Calculate the variance for a project with the following returns: 10 percent (Prob 0.5) and 20 percent (Prob 0.5).

In the context of the Total Probability Rule, what is P(S^c) if P(S) is 0.70?

Using the Total Probability Rule: P(Pass|Study) = 80 percent, P(Pass|Not Study) = 40 percent, P(Study) = 60 percent. What is the total probability of passing?

What does a node in a probability tree represent?

If P(A) = 0.5 and P(B|A) = 0.4, what is the joint probability P(AB)?

Bayes' Theorem helps us update the probability of a hypothesis based on what?

In Bayes' Theorem, the updated probability is also known as the:

You estimate the probability of EPS being 3 dollars at 25 percent and EPS being 4 dollars at 75 percent. What is the expected EPS?

Which calculator key is used to clear work in the STAT function of the TI BA II Plus?

Assume a scenario with a 60 percent probability of declining interest rates. If rates decline, there is a 75 percent chance EPS is 4 dollars. What is the joint probability of rates declining AND EPS being 4 dollars?

If the Expected Value is 15 and one observed outcome is 20 with a probability of 0.2, what is the squared deviation weighted by probability for this specific outcome?

A probability tree has two initial branches: A (30 percent) and B (70 percent). If branch A leads to outcome X with 50 percent probability, what is P(AX)?

In the formula for Bayes' Theorem, the numerator contains:

Given: P(Pass) = 68 percent. P(Pass|Study) = 80 percent. P(Study) = 70 percent. Calculate P(Study|Pass) using Bayes' Theorem.

Which of the following is true regarding standard deviation?

If the probability of studying is 70 percent, what is the probability of the complement (not studying)?

In a probability tree, if one branch has a probability of 40 percent, and the other branch represents the only other possibility, what is the probability of the second branch?

Calculate the expected return: Stock A (Return 5 percent, Prob 0.2), Stock B (Return 10 percent, Prob 0.3), Stock C (Return 20 percent, Prob 0.4), Stock D (Return 30 percent, Prob 0.1).

In the context of the FinTree Fruit 2 example, if earnings benefit from a declining interest rate, identifying the 'state' of the interest rate environment is an example of:

Which of the following values represents a valid variance?

Given P(A) = 0.4, P(B|A) = 0.5, and P(B|A^c) = 0.2, what is P(B)?

If we calculate a conditional mean, we are calculating the expected value:

When calculating variance using probabilities, the deviations are squared to:

If the Unconditional Probability of Passing is 0.68 and the Joint Probability of Passing AND Studying is 0.56, what is the Probability of Studying given Passing?

A 'Prior Probability' in Bayes' Theorem refers to:

If a stock has a 50 percent chance of returning 10 percent and a 50 percent chance of returning -10 percent, what is the expected return?

In the same stock scenario (50 percent chance of +10 percent, 50 percent chance of -10 percent), what is the variance?

Probability trees are particularly useful for visualizing:

In a probability tree, the sum of probabilities of all final outcomes (endpoints) must equal:

What is the standard deviation of a constant return (e.g., a guaranteed 5 percent)?

Given P(A) = 0.2 and P(B) = 0.3, if A and B are independent, what is P(A and B)?

If P(Info|Event) = 0.9, P(Event) = 0.1, and P(Info) = 0.2, what is P(Event|Info)?

A standard deviation of 7.75 corresponds to a variance of approximately:

Consider a probability tree where the first node splits into 'Study' (70 percent) and 'Not Study' (30 percent). If 'Not Study' branches into 'Pass' (40 percent) and 'Fail' (60 percent), what is the joint probability of 'Not Study and Fail'?

What is the primary difference between a conditional probability and a joint probability?

When using the Total Probability Rule to find P(Pass), we sum:

Given returns 5, 10, 20, 30 with probabilities 0.2, 0.3, 0.4, 0.1. Mean is 15. The squared deviation for return 10 is:

If E(X) = 15.40 percent and E(Y) = 10.30 percent, these values represent:

In a Bayes' scenario, if the likelihood of evidence given the event is 100 percent (certainty), the posterior probability depends on:

Calculate: P(A)=0.5, P(B|A)=0.2. What is P(AB)?

If a probability tree has 3 branches coming from a node, with probabilities 0.2, 0.3, and X. What is X?

Given Variance = 76. What is the approximate Standard Deviation?

In the HDFC Bank example, the 'Declining Interest Rate' scenario has a probability of 60 percent. This is best described as:

Which measure cannot be negative?

If P(A) = 0.5, P(B|A) = 0.5. What is P(AB)?

If you calculated a Posterior Probability of 1.2, what have you done wrong?