**Practice Problems for the Lander Math Contest**

**Module 13, Problems (40-42)**

40) 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 .