Stochastic Processes Flashcards
What is Stochastic Processes?
same observer responds in different ways to the same stimuli
Give example of Stochastic processes?
Rolling a dice as numbers are variable
How do you write what the probability of dice taking a 1?
P(X=1)
What is the probability of dice having 1
P(X=1) = 1/6
How can dice have same probability value?
As the dice is fair and X can take any value of the dice. have the same probability
What is X ?
X is a random variable, and a specific value.
What do all probabilities have?
Sum of 1 and no negative outcome = random variable
What is a random variable?
Probability has a sum of 1 and no negative outcome
What does E[X] mean ?
E[X] means expected value = mean of random variable
What is the E[X] of a dice?
E[X] = 1/6 +1/6 +1/6+1/6+1/6+1/6
mew = 3 1/2
What is the variance?
Average squared difference between each value and expectation
What is the variance of the dice?
sigma squared = 2 11/12
what is the expectation of two dice?
Expectation = E[X] = mean
= 3 1/2 x 2 = 7
what is the variance of two dice?
sigma squared = 2 11/12 x 2
= 5 5/6
What is the standard deviation?
sigma square root? = sqaure root 5 5/6
= 2.5
