# Question: Consider the random variable X with the probability density a Use

Consider the random variable X with the probability density

(a) Use the result of Example 7.2 to find the probability density of Y = | X|.

(b) Find the probability density of Z = X2(=Y2).

(a) Use the result of Example 7.2 to find the probability density of Y = | X|.

(b) Find the probability density of Z = X2(=Y2).

## Answer to relevant Questions

Consider the random variable X with the uniform density having α = 1 and β = 3. (a) Use the result of Example 7.2 to find the probability density of Y = | X|. (b) Find the probability density of Z = X4(=Y4). With reference to Example 3.12 on page 82, find (a) The probability distribution of U = X + Y; (b) The probability distribution of V = XY; (c) The probability distribution of W = X – Y. Consider two random variables X and Y whose joint probability density is given by Find the probability density of U = Y – X by using Theorem 7.1 as modified on page 216. Use the moment-generating function technique to rework Exercise 7.27. In exercise If X1 and X2 are independent random variables having binomial distributions with the respective parameters n1 and θ and n2 and θ, show that ...If X1 and X2 are independent random variables having exponential densities with the parameters θ1 and θ2, use the distribution function technique to find the probability density of Y = X1 + X2 when (a) θ1 ≠ θ2; (b) ...Post your question