Let X denote the  number of hours you study during a randomly selected school day. The  probability that X can take the values , has the following form where k is some unknown constant, $p\left(X=x\right)=\left\{\begin{array}{ccc}0.1& if& x=0\\ kx& if& x=1or2\\ k(5-x)& if& x=3or4\\ 0& & otherwise\end{array}\right.$What is the probability that you study at most two hours?

p(X=0) =0.1,                                       p(X=1) =kx = k(1)=k,                                          p(X=2)=kx= k(2)=2k,   

p(X=3)=k(5-x)= k(5-3)=2k,                  p(X=4)=k(5-x)=k(5-4)=k ,                                   p(x otherwise)=0     

p(S) =1

$\sum _{x_i}$p(X=x_i)=1

0.1+k+2k+2k+k+0=1

6k+0.1=1

6k=1-0.1

6k=0.9

k=$\frac{0.9}{6}$=0.15

Hence p(x$\le$2)=p(x=0)+p(x=1)+p(x=2)

= 0.1+k+2k=0.1+3k

0.1+3(0.15)

0.1+0.45=0.55