Probability

Question 1

State the value of XC0 where X is any number

Answer 1

Always 1

Question 2

Name the distribution where each variablein a discrete data set is equally likely to be chosen

Answer 2

Discrete uniform distribution

Question 3

What must be true in binomial distribution

Answer 3

Two outcomes
Probability of each event stays constant for each trial
Trials are independent
Variable must be discrete

Question 4

What do n and p mean in X~B(n, p)

Answer 4

n= number of trials
p= probability of success

Question 5

What is binomial PD used for

Answer 5

P(X=x)

Question 6

What are the features of discrete random variables

Answer 6

Set values

Sum of probabilities is 1

Question 7

What does |X–3| mean

Answer 7

Modulus X–3 (absolute value)

Question 8

What is the critical region

Answer 8

Where H0 is rejected

Question 9

When using cumulative probability why must f(2.6) be rounded to f(2) not f(3)

Answer 9

We don’t know the distribution up to 3 so must assume it’s the same as 2

Question 10

What is binomial CD used for

Answer 10

P(X

Question 11

When are two or one tail test used

Answer 11

Two tailed = determine bias

One tailed= determine what it’s biased towards

Question 12

What is the null hypothesis

Answer 12

Original probability

Question 13

What is the alternative hypothesis

Answer 13

Probability of Claim or suspicion

Question 14

When the probability is outside of the critical region what occurs

Answer 14

We fail to reject the null hypothesis

Question 15

What happens the the significance level in a two tailed test

Answer 15

Halfed (for split between top and bottom critical regions)

Question 16

Name the steps in testing a hypothesis

Answer 16

Set probability

State null and alternative hypothesis

State binomial distribution using P of null hypothese

Find P of unusual

Compare to significance level

State whether you reject or fail to reject the null hypothesis

State what this suggests in context

Question 17

What is the actual significance level

Answer 17

The probability as a percentage of:

the first value in the critical region at the higher end
or
the last value in the lower end

Question 18

How do you calculate the CR

Answer 18

List values of X and find cumulative probability

Values below SL (lower end) and values above 1 – SL (upper end) are in the critical region

Question 19

What is the difference between nPr and nCr

Answer 19

P= permutation so order matters

C= combination so order doesn’t matter

Question 20

P(X)=0.3
P(C)=0.6
X and C are mutually exclusive so find P(XUC)

Answer 20

0.3+0.6=0.9

Question 21

events O and Z are independent
find P(Z ⋂ O) if
P(O) =0.9 P(Z)=0.2

Answer 21

0.9x0.2=0.18

Question 22

How do you prove A and B are independent?

Answer 22

P(A)=P(A|B)

Question 23

How do you prove A and B are mutually exclusive?

Answer 23

P(AnB)=0

Question 24

Why is P(BnV)= P(V) x P(V|B) wrong?

Answer 24

it should be P(V) x P(B|V)

Question 25

What is the significance level?

Answer 25

The probability of rejecting the null hypothesis when it’s true