[" A random variable "x" has its range "{0,1,2,3.....}." If "P(x=r)=(c(r+1))/(2^(r))" for "r=0,1,2....],[" then "c=]

Suppose X is a random variable which takes values 0,1,2,3,.... and P(X=r)=pq^(r) , where 0ltplt1,q=1-p and r=0,1,2,...... then :

A random variable X has its range {-1,0,1} . If its mean is 0.2 and P(X=0)=0.2 ,then P(X=1)=

A: A random variable X has the range {1,2,3}. If P(X=1)=c, P(X=2)=3c,P(X=3)=6c then c=1//10 . R: If : S rarr R is a discreate random variable with range (x_(1), x_(2), x_(3),…………}" then" sum _(r=1)^(infty) (X=x)=1

If the range of the function F(x)=tan^(-1)(3x^(2)+bx+c) is [0,(pi)/(2)) (domain in R) then :

If the range of the function F(x)=tan^-1(3x^2+bx+c) is [0,pi/2) ; (domain in R) then :

If a,b,c are roots of x^3-px^2+qx-r=0 and r ne 0, then find (1)/(a^2)+(1)/(b^2)+(1)/(c^2) in terms of p,q,r.

C_(0)-C_(1)+C_(2)-C_(3)+......+(-1)^(r)C_(r)=((-1)^(r)(n-1)!)/(r!*(n-r-1)!)