X and Y are loss random variables, with X discrete and Y continuous. The joint density function of X and Y is f(x, y) = [(x+1)e-y/2] / 12 for x = 0, 1, 2 and 0 < y < [infinity]. Find the probability that the total loss, X + Y is less than 2.

The probability that the total loss, X + Y is less than 2 is P=0.235

Step-by-step explanation:

We know the joint density function:

To find the probability that (X+Y)<2, we can divide this in two steps.

- When X=0, Y should be less than 2. This is P(X=0,Y<2).

- When X=1, Y should be less than 1. This is P(X=1, Y<1).

We can calculate P(X=0,Y<2) as:

We can calculate P(X=1,Y<1) as:

Then

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4

step-by-step explanation:

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