Find the variance of the following distribution
`{:(,x_(i),2,3,11),(,f(x_(i)),1/3,1/2,1/6):}`

If the arithmetic mean of the following distribution is 8.2, then a = {:(x_(i) " :",1,3,5,9,11,13),(f_(i)" :",3,2,7,a,4,8):}

The variance of the random variable X having the following distribution is {:(X=x:,-2,-1,0,1,2),(P(X=x):,(1)/(6),(1)/(6),(1)/(3),(1)/(6),(1)/(6)):}

Find the domain of the following functions :(i)f(x)=sqrt(2x1)+sqrt(3-2x)

Find the inverse of the following functions(i) f(x)=sin^(-1)((x)/(3))x in[-3,3]

The median for the following frequency distribution is : {:(x_(i) " :",1,2,3,4,5,6,7,8,9),(f_(i)" :",8,10,11,16,20,25,15,9,6):}

Find the mean variance and standard deviation of the following probability distribution x_(i):aquad bpp_(i):pq where p+q=1

Find the variance and standard deviation of the random variable X whose probability distribution is given below : {:(x,0,1,2,3),(P(X=x),1/8,3/8,3/8,1/8):}

Find the domain and range of the following functions: (i) f(x) = sqrt((x-1) (3-x)) (ii) f(x) = 11-7 sin x (iii) f(x) = 1-|x|