Question

Let X and Y be random variables with joint density function

f(x, y) = 4xy, 0 < x, y < 1,
0, elsewhere.
Find the expected value of Z = √X²+Y².

Answer 1

The student's question pertains to calculating the expected value of a random variable Z which is a function of two other normally distributed random variables X and Y. The z-scores for specific values of X and Y are discussed, demonstrating the relationship between the value, the mean, and the standard deviation.

Step-by-step explanation:

The question deals with finding the expected value of random variables, specifically using the joint density function of two variables X and Y to calculate the expected value of Z, where Z is a function of both variables.

When dealing with normal distributions for X and Y, if X follows N(5, 6) and Y follows N(2, 1), we can calculate the z-score for a given value of X or Y. The z-score tells us how many standard deviations away from the mean a certain value is. For X = 17, the z-score is found to be 2, indicating that 17 is 2 standard deviations to the right of its mean. Similarly, for Y = 4, the z-score is also 2, meaning that 4 is 2 standard deviations to the right of its mean for Y.