(i) A real-valued function defined on the outcome of a probability experiment is

Question

(i) A real-valued function defined on the outcome of a probability experiment is called a _______ (ii) If X is a random variable, then the function F(x) defined by F(x) = P{X lessthanorequalto x} is called the _______ of X. (iii) A random variable whose set of possible values is either finite or countably infinite is called ______ (iv) If X is a discrete random variable, then the function p(x) = PX = x is called the _______ of X. The quantity E[X] defined by E[X] = sigma_x:p(x) > 0 xp(x) is called the _____ of X. (vi) The variance of a random variable X, denoted by Var (X), is defined by ________. (vii) A useful identity is Var(X) = _____ (viii) The quantity squareroot Var(X) is called the _____ of X.

Explanation / Answer

i) continuous random variable

ii) probability function for the random variable X

iii) discrete random variable

iv) probability mass function for the discrete random variable

v) Mean OR EXPECTATION OF X

vi) The average of the squared differences from the Mean. I.E Var(X)=E[ (X-[X]^2) ]

vii) var(x)= E[X^2] - E[X]^2

viii) standard deviation

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