ECON 5 Midterm

According to Bayes' Rule, P(A|B) equals what?

(P(B|A)P(A))/P(B)

What characteristics does the Bernoulli distribution have?

- Only 2 possible outcomes: success or failure - Probability of success and failure sum up to 1 - Analyzes a single success/failure scenario

Let X be a random variable such that E(X) = 2.5. Find E(0.5 + 3X)

8

Imagine that 1 in 5 individuals is allergic to peanuts. A peanut allergy test gives a positive result 10% of the time. If someone has a peanut allergy, the test will give a positive result 40% of the time. What is the probability that you have a peanut allergy if the test result is positive?

80%

True or false: If Y follows a normal distribution, then Y can only take positive values.

False

True or false: If the covariance between two random variables is 0, then these random variables are always statistically independent.

False

What does it mean when Cov(x,y) > 0?

x and y tend to move in the same direction

The mean of a uniform random variable with 4 as the minimum value and 6 as the max is:

5

Imagine P(A) = 0.25, P(B) = 0.8, and A and B are statistically independent. What is the probability of the intersection of A and B?

0.2

The odds of winning the lottery are 1 to 4. What is the probability of winning?

0.2

When you toss a coin, there are only two possible outcomes: heads and tails. The coin is NOT fair, and heads occur with a probability of 40 % and tails--with a probability of 60 %. Define a random variable X such that X = 1 if you obtain heads and X = 0 if you obtain tails. What is Var[X]?

0.24

Imagine P(A) = 0.7, P(B) = 0.1, and A and B are mutually exclusive. What is the probability of the union of A and B?

0.8

Imagine that, for your teaching assistant, the probability of drinking coffee in the morning is independent of whether they worked late the night before or not. The probability of having coffee in the morning is 40% and the probability of working late is 90%. What is the probability of drinking coffee in the morning given working late the night before?

40%

The area under the curve f(x) represents probability, what is the total area under the curve?

1

The variance of a uniform random variable with 4 are the min and 6 as the max is:

1/3

Let X be a random variable such that Var(X) = 3. Find Var(6X)

108

Let X be a random variable such that Var(X) = 169. Find the standard deviation of X.

13

When the correlation coefficient is 0, what could the scatter plot of x and y look like?

Horizontal line

The standardized random variable z has

Mean 0 and variance 1

When is a distribution symmetric?

Median = Mean

The conditional probability function of X, given Y = y is defined as...

P(x, y)/P(y)

What does a z-score of 0 indicate?

The value is equal to the mean

Consider A = [1, 2, 3, 5, 6] and B = [3, 4, 5, 7, 8]. Which is the intersection of A and B?

[3, 5]