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

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.