# Question

Use the formula obtained in Exercise 3.58 to verify the result of Exercise 3.55.

In exercise

If F(x, y) is the value of the joint distribution function of the two continuous random variables X and Y at (x, y), express P(a < X ≤ b, c < Y ≤ d) in terms of F(a, c), F(a, d), F(b, c), and F(b, d).

In exercise

If F(x, y) is the value of the joint distribution function of the two continuous random variables X and Y at (x, y), express P(a < X ≤ b, c < Y ≤ d) in terms of F(a, c), F(a, d), F(b, c), and F(b, d).

## Answer to relevant Questions

Use the formula obtained in Exercise 3.58 to verify the result of Exercise 3.57. In exercise If F(x, y) is the value of the joint distribution function of the two continuous random variables X and Y at (x, y), express P(a < ...With reference to Exercise 3.65, find P(X + Y < 1/2 ). In exercise Find k if the joint probability density of X, Y, and Z is given by With reference to Exercise 3.74, In exercise If the joint probability density of X and Y is given by Find (a) The marginal density of Y; (b) The conditional density of X given Y = 1. A coin is biased so that heads is twice as likely as tails. For three independent tosses of the coin, Find (a) The probability distribution of X, the total number of heads; (b) The probability of getting at most two heads. hThe total lifetime (in years) of five- year- old dogs of a certain breed is a random variable whose distribution function is given by Find the probabilities that such a five- year- old dog will live (a) Beyond 10 years; ...Post your question

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