If the range of X is the set {0, 1, 2, 3, 4} and P(X = x) = 0.2, determine the mean and variance of the random variable.

onetreehillyg

onetreehillyg

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2022-08-20

If the range of X is the set {0, 1, 2, 3, 4} and P(X = x) = 0.2, determine the mean and variance of the random variable.

Answer & Explanation

Pegoxv

Pegoxv

Beginner2022-08-21Added 7 answers

From the definition the probability mass function is:
f(x)={0.2x=0,1,2,3,40elsewhere
Use the definition of mean (3-3 in the text):
E(X)=xxf(x)
=0*0.2+1*0.2+2*0.2+3*0.2+4*0.2
=2
Use the definition of variance, often denoted with Var:
Var(X)=xx2f(x)E(X)2
=020.2+120.2+220.2+320.2+420.222
=6-4
=2
Result:
Use the definitions and equation (3-3) in the text.
Mean and variance are both 2

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