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?

Question

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?

sineurosi0f · Accepted Answer

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)=275−152=275−225=50  sd=Var(X)=50=7.07