a) Find P(Y_1 <= 3/4 , Y_2 >= 1/2)
b) Find P(Y_1 <= 3/4 , Y_2 <= 3/4)

Solution Preview

The easiest way to set up integral ranges is to actually draw a diagram of the domain of the function. Note that the domain is bounded by the square 0 <= y_1 <= 1, 0 <= y_2 <=1. So let's start by drawing that. Then because there's an additional constraint that y_1 <= y_2, you'll want to draw a diagonal line y_1 = y_2, and shade the upper triangle. (If you're ever doubtful regarding which region to shade, pick a random point in each region, and test to see if that point satisfies ...

Solution Summary

The easiest way to set up integral ranges is to actually draw a diagram of the domain of the function. From your graph, determine whether the region of integration is simple. If not, methodically divide the region into parts that are simple.

... problem is very simple and you don't want to go for complicated integration. ... Hence the joint probability density function of ( X 1 , X 2 ) is given by(using the ...

... The joint distribution function (jdf) is: (1.1) The ... of the unit circle, the integration limits are thus: (1.3) The conditional probability density is given ...

Double Integration : Joint PDF, Marginal and Conditional Densities. ... Y are continuous random variables with the joint probability density function k(x+y ...

Probability and conditional distributions ... l)y) be 9. Let f(x, y) ( ( the joint pili of ... whenever x and y simultaneously included in the integration) The marginal ...

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... be easily solved using the conditional probability theorem that ... 1)! out of the integral, and joining t and t ... This can be done using integration by parts several ...