How do you find the mean of the random variable x? X= 5,10,15,20,25 P(x) =...

Yahir Haas

Yahir Haas

Answered

2022-01-28

How do you find the mean of the random variable x?
X= 5,10,15,20,25
P(x) = 1/5, 1/5 , 1/5, 1/5, 1/5
What is the variance and standard deviation of the random variable x?
What is the standard deviation of the random variable x?

Answer & Explanation

sineurosi0f

sineurosi0f

Expert

2022-01-29Added 14 answers

mean E(X)=15
Var(X)=50
sd=7.07
Explanation:
For a probability distribution
E(X)=allxxP(X=x)...(1)
in this case we have
E(X)=5×15+10×15+15×15+20×15+25×15
E(X)=1+2+3+4+5
E(X)=15
the variance is calculated by
Var(X)=E(X2)E(X)...(2)
where E(X2)=allxx2P(X=x)...(3)
E(X2)=52×15+102×15+152×15+202×x15+252×15
E(X)=15(25+100+225+400+625)
E(X2)=275.
Var(X)=275152=275225=50
sd=Var(X)=50=7.07

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