If a curve X has probability density function (pdf)
`f(x)={{:(ax","0lexle1),(a","1lexle2),(3a-ax","2lexle3),(0",""otherewise"):}`
Then, a is equal to

Let f(x)={{:(1-x,0lexle1,),(0,1lexle2,),((2-x)^(2),2lexle3,):} , then 6int_(0)^(3)f(x)dx is equal to-

If f(x)={{:(x",",0lexle1),(x+a",",xgt1):} then

If f(x)={{:(3x^(2)+12x-1",",-1lexle2),(37-x",",2ltxle3):} , Then

int_(1)^(4)f(x)dx where f(x)={:{(4x+3",",1lexle2),(3x+5",",2lexle4):}

If a random variable waiting time in minutes for bus and probability density function of x is given by f(x)={{:(1/5","0lexle5),(0",""otherwise"):} Then probability of waiting time not more than 4 minutes is equal to

Verify Rolle's Theorem for the function : f(x)={{:(-4x+5", "0lexle1),(2x-3" , "1ltxle2):}

Evaluate int_(0)^(3)f(x)dx , where f(x)={:{(x+3,0lexle2),(3x" ",2lexle3):}

Let the function f be defined by f(x)={(3x0lexle1),(-3x+51ltxle2):} , then:

The function f defined f(x){(x[x],0lexle2),((x-1)x,2lexlt3):} , Then Lf'(2) =

Dicuss the continuity of the function: f(x)={{:(1+x^(2)", "0lexle1),(2-x", "xgt1):} at x = 1.