Let X denote the number of hours you study during a randomly selected school day The probability that X can take the values x. has the following form, where k is some unknown constant. `P(X=x)={0. 1 ,""""if""""x=0k x ,""""if""x=1""""or""""2k(5-x)

Explanation

a)
`sum_(all x)P(X=x)=1`

`0.1+k+2k+2k+k=1`

`0.1+6k=1`

`6k=0.9`

`k=0.9/6=0.3/2=0.15`

b)`P(x>=2)=P(x=2)+P(x=3)+P(x=4)`

`=0.3+0.3+0.15`

...