Let x and y each be random real numbers chosen from the uniform interval (0,1). Call the product of these numbers z.

1) Find the probability that z is in the interval (.1,.2)

2) Find the probability that z is any decimal whose first digit when written in scientific notation is a 1.

Bonus) Find the full probability distribution of the first digit of z.

Note: Give all answers as exact numbers in closed form.

(3)The required probability distribution is as follows:

Edited on February 23, 2024, 11:58 pm

Posted by K Sengupta on 2024-02-23 23:54:50