Let ,f( x) = [1 [34 (2x - x2) if Os x= 20otherwise f(x)={34 (2x -x2 ) if Osxs20oth erwise 1 Show that f( x )f(x) is a probability density function . 2. Find P(X = 0.25 )P(X=0.25 ). Find P(X = 1.4 ) P (X21.4). Find P(0.1 = X = 1.2 ) P(0.1 SX$1.2 ). Determine the mean value of XX. Let,f(x) = [|1 | |4In (3)(4x + x2)if 1= x= 60otherwise f(x)={4In (3) (4x +x2 ) if 1 Exs 60otherwise Show that f(x )f(x) is a probability density function . NP Find P(X= 1)P(Xs1). Find P(X = 5 ) P (X25). UAW Find P(1 = X= 5 )P(15X$5). Determine the mean value of XX. [ Let, f(x) = 1 (110 ( 1 + sin ( nx - 12 )) if Os x 100otherwise f(x)={110 (1 + sin (nx - 12 ))if Osx 100otherwise Show that f(x ) f(x) is a probability density function Find P(X = 3)P(X