Probability

Question 1

What is probability?

Answer 1

the ratio of having a particular outcome among all possible outcomes would converge to a certain number between zero
and one

Question 2

What is the alternative view of probability?

Answer 2

a measure of belief about the predicted outcome of an event.

Question 3

What is a discrete random variable

Answer 3

can take on a finite or countably infinite number of distinct values.

Question 4

What is probability mass function

Answer 4

Function that gives the probability that a discrete random variable is exactly equal to some value

Question 5

What is a continuous random variable

Answer 5

A continuous random variable in statistics is a variable that can take any value within a certain range or interval. Unlike discrete random variables, which can only take on specific, distinct values, continuous random variables can take on an infinite number of values within a given range.

Question 6

Probability distribution function

Answer 6

a function that describes the likelihood of a continuous random variable taking on a particular value or falling within a particular range of values.

Question 7

What is binomial distribution?

Answer 7

counts the total number of successes out of n trials, where X is the number of successes.

Question 8

Characteristics of binomial distribution

Answer 8

• Each trial must be independent of the previous trial/experiment
• The probability of success must be the same for each trial

Question 9

Set of assumptions required for binomial distribution

Answer 9

1. A set of n experiments or trials are conducted
2. Each trial could result in either a success or a failure
3. The probability p of success is the same for all trials
4. The outcomes of different trials are independent
5. We are interested in the total number of successes in these n trials.

Question 10

What is the binomial distribution formula?

Answer 10

P(x) = (n! / x!(n-x)!) * p^x*q^n-x
n = number of trials or number getting sampled
x = the number of successes desired
p = probability of success
q = 1-p

Question 11

The probability of observing any sequence of n independent trials that contain x successes and n-x failures is

Answer 11

p^n * (1-p)^n-x

Question 12

Total number of possible sequences

Answer 12

n! / x! * (n-x)!

Question 13

When does binomial distribution attain it’s peak?

Answer 13

at p times n

Question 13

What is poisson distribution?

Answer 13

a probability distribution used to model the number of events that occur in a fixed interval of time or space when the events happen independently and at a constant average rate