Binomial Poisson

Which of the following is NOT an assumption of the Binomial distribution?

• All trials must be independent.

• Each trial must be classified as a success or a failure.

• All trials are dependent on each other.

• The number of successes in the trials is counted.

What is the expected value, E(x), for a binomial distribution?

• E(x) = n · p

• E(x) = n · 𝜎

Answer explanation

The expected value or mean of a binomial distribution is:

E(x) = n · p

This means (# of trials)(probability of success).

For example, the expected value for getting heads from 10 coin flips is:

10 (0.5) = 5 heads

Or

10 coins flipped (5 heads/10 coins flipped)

What is the variance for a binomial distribution?

Answer explanation

The variance for a binomial distribution can be thought of as:

EV · (probability of FAILURE)

What is an interesting feature of the Poisson distribution?

• The variance = the mean

• The variance = the standard deviation

• The variance = 1

What is the expected value of a Poisson distribution?

What type of distribution models this scenario? The mean number of accidents per month at a certain intersection is 3. What is the probability that in any given month exactly 4 accidents will occur at this intersection?

• Uniform

• Binomial

• Poisson

• Normal

Answer explanation

Whenever data is given as "mean number of ____ per month..." that means it's an average rate, and it can be modeled by a Poisson distribution.

The mean number of accidents per month at a certain intersection is 3. What is the probability that in any given month exactly 4 accidents will occur at this intersection?

• 0.815

• 0.647

• 0.168

• 0.352

Answer explanation

Use a Poisson PDF on your calculator:

𝞴 = 3

x = 4

• 0.168
• 0.147
• 0.944
• 0.294

• E(X)=16    sd = 2
• E(X)=8      sd = 2
• E(X)=8     sd = 1/2
• E(X)=16   sd = 1/2

• 0.490
• 0.224
• 0.180
• 0.423