stats MCQ test

what is the formula for variance

for binomial its: np(1−p)

how to find a joint pdf qu 14

fx(x) times fy(y)

find a formula in terms of x and y

find the jacobean

jacobean times by fx(x)fy(y)

how to find MGF

how to find pdf with 2 different variables

find pdf

use P(Y<= y) = P(X²<= Y)

find cdf by intergrating

sub in x values

find pdf by differentiating

how would you find a var with multiple independent variables

use this formula a the start and end for final answer

1.find fx(x) and fy(y)

2. find E[x] and E[x²] by intergaring fx(x) times by x²/x

3.use formula to find var[x]

Top tips to get max marks for question 1 in final exam

• always write the pdf with value subbed then working out

How do you answer a) b) and c)

a) Intergrate using limits, the intergral is equal to 1

b) E[X] = intergral(xf(x)) , E[X] = intergral(x² f(x)), Var(X) = E[X²] − (E[X])2

c) FY​(y)=P(X³≤y)=P(X≤y^1/3)

Intergrate and plug in limits

fY​(y)= d/dy (intergal) x∈(a,b)

Apply continuity correction

How do you solve C when there are no limits

1. Isolate X in terms of y

2. dx/dy = a

how would you solve a question such as this

a) find fx(x) by integrating the joint pdf in terms of y

fy(y) by integrating the joint pdf in terms of x

b) then fxy(x,y)/fx ALWAYS INCLUDE LIMITS

c) find upper bound by subbing in value in question

• sub in x value into fxy(x,y)/fx

• integrate with limits

state the quotient rule

when should you use this property L’(t) being the log differential of M(t)

When M(t) involves e

MGF vs PGF

when finding E[X] and VAR[X]

How to find Var(x) and E(x) from PDF