Question

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=0,k x if x=1 , 2k(5-x) if x=3 or 4, 0 otherwise Select the correct answer from above options

Answer 1

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` `=0.75` `P(x=2)=0.3` `P(x<=2)=P(x=0)+P(x=1)P(x=2)`<br> `=0.1+0.15+0.3` `=0.55`