Random Variables and Distributions

From outcomes to numbers

Densities for continuous values

The distribution function

Joints, marginals and sums

A fair coin is flipped three times and S counts heads. Using the binomial distribution with n equal to 3 and p equal to one half, what is the probability of exactly two heads?

A fair coin is flipped until the first head appears. What is the probability that the first head comes on exactly the third flip?

Let X have a Poisson distribution with parameter lambda equal to 2. Which expression gives the probability that X equals 0?

Let X be exponential with rate lambda equal to 2. Which expression gives the probability that X is at most 1?

X is uniform on the interval from 0 to 4. Using the distribution function, what is the probability that X lies between 1 and 3?

U and V are independent and uniform on the interval from 0 to 1. Using the triangular density of the sum, what is the density of U plus V evaluated at 1.5?

A fair coin is flipped three times. Compute the probability of exactly one head using the binomial distribution and write the number, either as a decimal or as a fraction.

X is uniform on the interval from 0 to 4. Compute the probability that X is at most 1 and write the number, either as a decimal or as a fraction.

U and V are independent uniforms on the interval from 0 to 1. Compute the density of U plus V at the point 0.5 and write the number, either as a decimal or as a fraction.