# Topic 3: Discrete and continuous probability distributions

### Week 4

Hello,

In this week you will learn how to calculate the mean and variance of a discrete distribution, probabilities based on binomial data and lastly probabilities based on the normal distribution.

## Question 1

Consider a discrete random variable X:

X          p(X)

0          0.3

1          0.2

2          0.1

4          0.4

Derive the population mean (mu) i.e. E(X) and the variance and standard deviation.

## Question 2

You and two friends go to a pretty unreliable fast-food franchise, which last month filled 90% of orders correctly.  What is the probability that

a. all three orders will be filled correctly?

b. none of the three will be filled correctly?

c. at least two of the three will be filled correctly?

## Question 3

Given the standard normal distribution, what is the probability that

a. Z < 1.57

b. Z > 1.84

c. 1.57 < Z < 1.84

## Question 4

Given a normal distribution with a mean of 100 and a standard deviation of 10, what is the probability that

a. X > 75?

b. 80% of the values are between what two X values (symmetrically distributed around the mean)?