Assignment 4 Problem 1

Consider an experiment in which each of \({{ params.numVehicles }}\) vehicles taking a particular highway exit either turn left (L) or right (R) at the end of the exit ramp. Let \(X\) be a random variable that counts the number of right turns made by the \({{ params.numVehicles }}\) observed vehicles. Please round all answers and probabilities to 3 decimal places.

Part 1

(1 point) Suppose that 71.0% of cars turn right at this particular highway (and 29.0% of cars turn left). Assuming cars are independent, what distribution does \(X\) follow?

Answer Section

• Bernoulli

• Binomial

• Poisson

• Normal

• Hypergeometric

Part 2

(3 points) Provide the pmf of \(X\) in table form (round probabilities to 3 decimal places). Enter the probabilities in the matrix below. Ex. [P(X=0), P(X=1), P(X=2), …].

Part 3

(1 point) What is \(E\[X\]\)?

Part 4

(1 point) What is \(Var(X)\)?

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.