Discrete random variables

Question 1

How is the expected values of discrete random variable X written as and how is it calculated

Answer 1

E(X)
E(X) = ∑ x(i)p(i) where x(i) is each possible value that X can take and p(i) is its associated probability.

Question 2

How is the variance of a discrete random variable X written as and how is it calculated

Answer 2

Var(X)
Var(X) = E(X^2)-(E(X))^2
where E(X^2)= ∑x^2(i)p(i)

Question 3

What is the mode of a discrete random variable X

Answer 3

The value of X associated with the largest probability

Question 4

What is the median M of a discrete random variable X.

Answer 4

The Value of X such that
P(X≤M)≥0.5 and P(X≥M)≥0.5
If there are 2 possible values, the mean of them must be taken

Question 5

If X is a random variable and Y is a new radom variable such that Y= aX +b then what is
a) E(Y)
B) Var(Y)

Answer 5

a) aE(X)+b
b)a^2Var(X)

Question 6

If X is a discrete random variable with expectation E(X) and g is a function applied to X then what is E(g(X))=

Answer 6

∑g(x(i))p(i)

Question 7

What is an example of a Uniform discrete distribution

Answer 7

Rolling a fair dice (The probability of all evvents accuring are equal)

Question 8

For a uniform discrete distribution, the P(X=x)=

Answer 8

1/n

Question 9

For a uniform discrete distribution X~U(n), what is E(X)

Answer 9

n+1/2

Question 10

For a uniform discrete distribution X~U(n), what is Var(X)

Answer 10

n^2-1/12