Practice Problems for  the Lander Math Contest
Module 13, Problems (40-42)

Let the probability density function for the random variable
0<x<1 is the straight line f(x)=-2x+2. The value of f(x) outside
the interval (0,2) is equal to zero. Find the probability that
randomly chosen x will be between 0.5 and 1.

41) Calculate all probabilities of getting heads (0,1,…,6
heads) for the fair coin if the number of tosses is 6.

42) Solve the previous problem for an unfair coin with P(H)=
0.75 .