Prob&Stats

Binomial distribution formula

Equation for conditional probability

Moment generating function

moment generating fucntion for descrete variable

Derivative facts about moment generating function

How to find vaiance using MGS

moment generating fucntion for contrinious variables

What condition is required so, that : MGF of a sum of independent random variables=product of their MGFs

mutually independent and identically distributed

How to work out standard error

how to find unbiased sample variance

How do I decide whether a random variable is discrete or continuous?

Discrete: takes countable values, usually counts. e.g. 0,1,2,3
Continuous: can take any value in an interval.

What is the Poisson probability formula?

When can I model a count using a Poisson distribution?

• Constant average rate.

• Independent counts in non-overlapping intervals.

• Probability depends only on interval length, not location.

• In a very small interval, probability of one event is approximately proportional to interval size.

• Probability of two or more events in a very small interval is negligible.

When do I use the binomial distribution?

1. fixed number of trials n

2. each trial has 2 outcomes - failure/ success

3. Same success probability each trial

4. Trials are independent

How do I standardise a normal variable?