# Probability and Statistics Calc Based

• I-aM-Lost
In summary, probability is the study of the likelihood of events occurring, while statistics involves analyzing and interpreting data. Calculus is used in probability and statistics to calculate probabilities of continuous events and to find the area under a curve. The mean, median, and mode can be calculated by finding the average, middle value, and most frequently occurring value in a data set, respectively. The central limit theorem states that the means of independent samples from a population will be normally distributed, allowing for inferences to be made about the population based on a sample. Two events are considered independent in probability if the probability of one event occurring does not affect the probability of the other event occurring, which can be determined by comparing the joint probability to the individual probabilities.
I-aM-Lost

## Homework Statement

that it is exact...
[/B]
X and Y are discrete random variables with joint pmf

Chart attached

(a) Find V ar(X) and Var(Y).
(b) Find Cov(X; Y).
(c) Find the correlation of X and Y.
(d) Find the conditional distribution of X given that Y= 3

## Homework Equations

Trying to check my answers to see if i am correct.

## The Attempt at a Solution

[/B]
a. Var(x) = 0.8 Var(Y) = 1
b. 0.4
c. 0.1414
d. 1/5;1/5;3/5

Thanks

What is pmf?

Dr. Courtney said:
What is pmf?
probability mass function

## 1. What is the difference between probability and statistics?

Probability is the study of the likelihood or chance of events occurring, while statistics is the collection, analysis, and interpretation of data to make inferences about a population.

## 2. What is the purpose of using calculus in probability and statistics?

Calculus is used in probability and statistics to determine the probability of continuous events and to calculate the area under a curve, which is often used to represent probability distributions.

## 3. How do you calculate the mean, median, and mode of a set of data?

The mean is calculated by finding the sum of all the data points and dividing by the total number of data points. The median is the middle value when the data is arranged in ascending or descending order. The mode is the most frequently occurring value in the data set.

## 4. What is the central limit theorem and why is it important?

The central limit theorem states that the means of a large number of independent samples from a population will be approximately normally distributed, regardless of the shape of the population's distribution. This is important because it allows us to make inferences about a population based on a sample, which is often more feasible and less costly.

## 5. How do you determine if two events are independent in probability?

Two events are considered independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be determined by calculating the joint probability of the two events and comparing it to the individual probabilities of each event. If the joint probability is equal to the product of the individual probabilities, then the events are independent.

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