stats

Question 1

What is the formula for expectation

Answer 1

∑XP

Question 2

what is the formula for variance

Answer 2

Expectation(x²) - Expectation(x)²

Question 3

If one random variable Y is related to another random variable X by a linear relationship i.e. of the form Y = aX + b
what is the expectation and variance

Answer 3

E(aX+b) = aE(x)+b
Var(aX+b)= a² (Var(X))

Question 4

If 2 random variables are combined what is the expectation

Answer 4

E(x₁±x₂) = E(x₁)±E(x₂)

Question 5

If 2 random variables are combined what is the variance

Answer 5

Var(x₁±x₂) = Var(x₁)+Var(x₂)

Question 6

If 2 random variables in the form aX + bY are combined what is the expectation and variance

Answer 6

E(aX±bY) = aE(X) ±bE(Y)

Var(aX±bY) = a²Var(X) +b²Var(Y)

Question 7

When is binomial used

Answer 7

There are n independent trials
There are just two possible outcomes to each trial, success and failure,with fixed probabilities of p and q respectively, where q = 1 – p.

Question 8

What is the mean of binomial

Answer 8

NP

Question 9

What is the variance of binomial

Answer 9

NPQ

Question 10

What is the formula for binomial

Answer 10

NcR * P^r*(q)^n-r

Question 11

When is poisson used

Answer 11

Randomly
Independently
At a uniform average rate
It is an infinite probability distribution

Question 12

What is the mean of poisson

Answer 12

λ

Question 13

What is the variance of poisson

Answer 13

λ

Question 14

What is the formula for poisson

Answer 14

(e^-λ λ^r)/r!

Question 15

When is geometric used

Answer 15

Infinite
Probability of success on nth attempt is
2 Fixed possibilities success or failure
independent number of trials which continue until success is obtained

Question 16

What is the mean of geometric

Answer 16

1/p

Question 17

what is the variance of geometric

Answer 17

Q/p²

Question 18

what is the formula for geometric

Answer 18

(Q)^x-1p

Question 19

what is the cumulative formula for geometric

Answer 19

1-(q)^x