Final answer:
The probability that X is smaller than Y can be found by summing up the probabilities of all possible values of X that are smaller than Y.
Step-by-step explanation:
The subject of this question is Mathematics and it is of High School level.
The problem states that X is a random variable following a geometric distribution with parameter a, and Y is a random variable following a geometric distribution with parameter b. They are independent of each other.
To find the probability that X is smaller than Y, we need to calculate the probability p(X
We can solve this problem by using the definition of the geometric distribution and summing up the probabilities of all possible values of X that are smaller than Y.
Let's assume x is a non-negative integer. The probability that X=x can be calculated as P(X=x)=a(1-a)^(x-1).
Similarly, the probability that Y=y can be calculated as P(Y=y)=b(1-b)^(y-1).
We need to find the sum of probabilities p(X